Question 116585

{{{x^2+12x=-13}}} Start with the given equation



Take half of the x coefficient 12 to get 6 (ie {{{12/2=6}}})

Now square 6 to get 36 (ie {{{(6)^2=36}}})




{{{x^2+12x+36=-13+36}}} Add this result (36) to both sides. Now the expression {{{x^2+12x+36}}} is a perfect square trinomial.





{{{(x+6)^2=-13+36}}} Factor {{{x^2+12x+36}}} into {{{(x+6)^2}}}  (note: if you need help with factoring, check out this <a href=http://www.algebra.com/algebra/homework/playground/change-this-name4450.solver>solver</a>)




{{{(x+6)^2=23}}} Combine like terms on the right side


{{{x+6=0+-sqrt(23)}}} Take the square root of both sides


{{{x=-6+-sqrt(23)}}} Subtract 6 from both sides to isolate x.


So the expression breaks down to

{{{x=-6+sqrt(23)}}} or {{{x=-6-sqrt(23)}}}



So our answer is approximately

{{{x=-1.20416847668728}}} or {{{x=-10.7958315233127}}}


Here is visual proof


{{{ graph( 500, 500, -12, 10, -10, 10, x^2+12x+13) }}} graph of {{{y=x^2+12x+13}}}



When we use the root finder feature on a calculator, we would find that the x-intercepts are {{{x=-1.20416847668728}}} and {{{x=-10.7958315233127}}}, so this verifies our answer.