Question 114754


{{{x^2+8x+13=0}}} Start with the given equation



{{{x^2+8x=-13}}} Subtract 13 from both sides



Take half of the x coefficient 8 to get 4 (ie {{{8/2=4}}})

Now square 4 to get 16 (ie {{{(4)^2=16}}})




{{{x^2+8x+16=-13+16}}} Add this result (16) to both sides. Now the expression {{{x^2+8x+16}}} is a perfect square trinomial.





{{{(x+4)^2=-13+16}}} Factor {{{x^2+8x+16}}} into {{{(x+4)^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+4)^2=3}}} Combine like terms on the right side


{{{x+4=0+-sqrt(3)}}} Take the square root of both sides


{{{x=-4+-sqrt(3)}}} Subtract 4 from both sides to isolate x.


So the expression breaks down to

{{{x=-4+sqrt(3)}}} or {{{x=-4-sqrt(3)}}}



So our answer is approximately

{{{x=-2.26794919243112}}} or {{{x=-5.73205080756888}}}


Here is visual proof


{{{ graph( 500, 500, -10, 10, -10, 10, x^2+8x+13) }}} graph of {{{y=x^2+8x+13}}}



When we use the root finder feature on a calculator, we would find that the x-intercepts are {{{x=-2.26794919243112}}} and {{{x=-5.73205080756888}}}, so this verifies our answer.