Question 119461


*[Tex \LARGE (x+13)^2=25] Start with the given equation




*[Tex \LARGE x+13=\pm sqrt{25}] Take the square root of both sides





*[Tex \LARGE x+13=\pm 5] Simplify the square root (note: If you need help with simplifying the square root, check out this <a href=http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver> solver</a>)




*[Tex \LARGE x=-13\pm 5] Subtract 13 from both sides to isolate x.



 Break down the expression into two parts:




 <pre>

 *[Tex \LARGE x=-13+5]  <font size="6">or</font>  *[Tex \LARGE x=-13-5]

 </pre>


 Now combine like terms for each expression:

 <pre>

 *[Tex \LARGE x=-8]  <font size="6">or</font>   *[Tex \LARGE x=-18]   </pre>



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Answer:

So our solution is

 <pre>

*[Tex \LARGE x=-8]  <font size="6">or</font>   *[Tex \LARGE x=-18]

 </pre>


 Notice when we graph the equations {{{y=(x+13)^2}}} and {{{y=25}}}  we get:


{{{drawing(500, 500, -23, -3, -10, 30,
graph( 500, 500, -23, -3, -10, 30, (x+13)^2,25)
)}}} graph of  {{{y=(x+13)^2}}} (red) and {{{y=25}}} (green)




Here we can see that the two equations intersect at x values of {{{x=-8}}} and {{{x=-18}}}, so this verifies our answer.