Question 104634

*[Tex \LARGE (x+4)^2=81] Start with the given equation




*[Tex \LARGE x+4=\pm sqrt{81}] Take the square root of both sides





*[Tex \LARGE x+4=\pm 9] 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=-4\pm 9] Subtract 4 from both sides to isolate x.



 Break down the expression into two parts:




 <pre>

 *[Tex \LARGE x=-4+9]  <font size="6">or</font>  *[Tex \LARGE x=-4-9]

 </pre>


 Now combine like terms for each expression:

 <pre>

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



-----------------------------------

Answer:

So our solution is

 <pre>

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

 </pre>


 Notice when we graph the equations {{{y=(x+4)^2}}} and {{{y=81}}}  we get:


{{{drawing(500, 500, -18, 10, -10, 86,
graph( 500, 500, -18, 10, -10, 86, (x+4)^2,81)
)}}} graph of  {{{y=(x+4)^2}}} (red) and {{{y=81}}} (green)




Here we can see that the two equations intersect at x values of {{{x=5}}} and {{{x=-13}}}, so this verifies our answer.