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2015-06-01T05:50:31Z

Created page with "<span class="exam"> Solve. <math>\sqrt{x - 3} + 5 = x</math> {| class="mw-collapsible mw-collapsed" style = "text-align:left;" ! Foundations |- |1) How do you solve for <math>..."

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<span class="exam"> Solve. <math>\sqrt{x - 3} + 5 = x</math>
{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
! Foundations
|-
|1) How do you solve for <math> x </math> in the equation <math>\sqrt{x}=5 </math>?
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|2) How do you find the zeros of <math>f(x)=x^2+x-6</math>?
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|Answer:
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|1) You square both sides of the equation to get <math>x=25</math>.
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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>.
|}

Solution:

{| class = "mw-collapsible mw-collapsed" style = "text-align:left;"
! Step 1:
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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>.
|
|}

{|class = "mw-collapsible mw-collapsed" style = "text-align:left;"
! Step 2:
|-
|Now, to get rid of the square root, we square both sides of the equation.
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|So, we get <math>x-3=(x-5)^2</math>.
|}

{|class = "mw-collapsible mw-collapsed" style = "text-align:left;"
! Step 3:
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|We multiply out the right hand side to get <math>x - 3 = x^2-10x+25</math>.
|}

{|class = "mw-collapsible mw-collapsed" style = "text-align:left;"
! Step 4:
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|Getting all the terms on one side, we have <math>0=x^2-11x+28</math>.
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|To solve, we can factor to get <math>0=(x-7)(x-4)</math>.
|}

{|class = "mw-collapsible mw-collapsed" style = "text-align:left;"
! Step 5:
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|The two possible solutions are <math>x=7 </math> and <math>x=4</math>.
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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.
|-
|Thus, the only solution is <math>x=7 </math>.
|}

{|class = "mw-collapsible mw-collapsed" style = "text-align:left;"
! Final Answer:
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|<math>x=7 </math>
|}

[[004 Sample Final A|<u>'''Return to Sample Exam</u>''']]

004 Sample Final A, Problem 16 - Revision history

MathAdmin: Created page with " Solve. \sqrt{x - 3} + 5 = x {| class="mw-collapsible mw-collapsed" style = "text-align:left;" ! Foundations |- |1) How do you solve for ..."

MathAdmin: Created page with " Solve. $\sqrt{x - 3} + 5 = x$ {| class="mw-collapsible mw-collapsed" style = "text-align:left;" ! Foundations |- |1) How do you solve for $..."$