Question 147429


*[Tex \LARGE (x+6)^2=4] Start with the given equation




*[Tex \LARGE x+6=\pm sqrt{4}] Take the square root of both sides





*[Tex \LARGE x+6=\pm 2] 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=-6\pm 2] Subtract 6 from both sides to isolate x.



 Break down the expression into two parts:




 <pre>

 *[Tex \LARGE x=-6+2]  <font size="6">or</font>  *[Tex \LARGE x=-6-2]

 </pre>


 Now combine like terms for each expression:

 <pre>

 *[Tex \LARGE x=-4]  <font size="6">or</font>   *[Tex \LARGE x=-8]   </pre>



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Answer:

So our solution is

 <pre>

*[Tex \LARGE x=-4]  <font size="6">or</font>   *[Tex \LARGE x=-8]

 </pre>


 Notice when we graph the equations {{{y=(x+6)^2}}} and {{{y=4}}}  we get:


{{{drawing(500, 500, -13, 1, -10, 9,
graph( 500, 500, -13, 1, -10, 9, (x+6)^2,4)
)}}} graph of  {{{y=(x+6)^2}}} (red) and {{{y=4}}} (green)




Here we can see that the two equations intersect at x values of {{{x=-4}}} and {{{x=-8}}}, so this verifies our answer.