Difference between revisions of "004 Sample Final A, Problem 16"

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(Created page with "<span class="exam"> Solve. <math>\sqrt{x - 3} + 5 = x</math>")
 
 
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<span class="exam"> Solve. <math>\sqrt{x - 3} + 5 = x</math>
 
<span class="exam"> Solve. <math>\sqrt{x - 3} + 5 = x</math>
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{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
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! Foundations
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|-
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|1) How do you solve for <math> x </math> in the equation <math>\sqrt{x}=5 </math>?
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|-
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|2) How do you find the zeros of <math>f(x)=x^2+x-6</math>?
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|-
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|Answer:
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|-
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|1) You square both sides of the equation to get <math>x=25</math>.
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|-
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|2) You factor <math>f(x)=0</math> to get <math>(x+3)(x-2)=0</math>. From here, we solve to get <math>x=-3 </math> or <math>x=2</math>.
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|}
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Solution:
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{| class = "mw-collapsible mw-collapsed" style = "text-align:left;"
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! Step 1:
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|-
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|First, we get the square root by itself. Subtracting 5 from both sides, we get <math>\sqrt{x - 3}= x-5</math>.
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|
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|}
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{|class = "mw-collapsible mw-collapsed" style = "text-align:left;"
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! Step 2:
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|-
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|Now, to get rid of the square root, we square both sides of the equation.
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|-
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|So, we get <math>x-3=(x-5)^2</math>.
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|}
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{|class = "mw-collapsible mw-collapsed" style = "text-align:left;"
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! Step 3:
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|-
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|We multiply out the right hand side to get <math>x - 3 = x^2-10x+25</math>.
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|}
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{|class = "mw-collapsible mw-collapsed" style = "text-align:left;"
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! Step 4:
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|-
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|Getting all the terms on one side, we have <math>0=x^2-11x+28</math>.
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|-
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|To solve, we can factor to get <math>0=(x-7)(x-4)</math>.
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|}
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{|class = "mw-collapsible mw-collapsed" style = "text-align:left;"
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! Step 5:
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|-
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|The two possible solutions are <math>x=7 </math> and <math>x=4</math>.
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|-
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|But, plugging in <math>x=4 </math> into the problem, gives us <math> 6=\sqrt{4-3}+5=4 </math>, which is not true.
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|-
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|Thus, the only solution is <math>x=7 </math>.
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|}
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{|class = "mw-collapsible mw-collapsed" style = "text-align:left;"
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! Final Answer:
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|-
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|<math>x=7 </math>
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|}
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[[004 Sample Final A|<u>'''Return to Sample Exam</u>''']]

Latest revision as of 16:14, 3 May 2015

Solve. Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sqrt{x - 3} + 5 = x}

Foundations
1) How do you solve for Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x } in the equation Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sqrt{x}=5 } ?
2) How do you find the zeros of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f(x)=x^2+x-6} ?
Answer:
1) You square both sides of the equation to get Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x=25} .
2) You factor Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f(x)=0} to get Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (x+3)(x-2)=0} . From here, we solve to get Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x=-3 } or Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x=2} .


Solution:

Step 1:
First, we get the square root by itself. Subtracting 5 from both sides, we get Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sqrt{x - 3}= x-5} .
Step 2:
Now, to get rid of the square root, we square both sides of the equation.
So, we get Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x-3=(x-5)^2} .
Step 3:
We multiply out the right hand side to get Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x - 3 = x^2-10x+25} .
Step 4:
Getting all the terms on one side, we have Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 0=x^2-11x+28} .
To solve, we can factor to get Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 0=(x-7)(x-4)} .
Step 5:
The two possible solutions are Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x=7 } and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x=4} .
But, plugging in Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x=4 } into the problem, gives us Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 6=\sqrt{4-3}+5=4 } , which is not true.
Thus, the only solution is Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x=7 } .
Final Answer:
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x=7 }

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