SOLUTION: Solve the equation by completing the square x^2+12x= -13

Algebra ->  Square-cubic-other-roots -> SOLUTION: Solve the equation by completing the square x^2+12x= -13      Log On


   

Question 116585: Solve the equation by completing the square
x^2+12x= -13
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2%2B12x=-13 Start with the given equation


Take half of the x coefficient 12 to get 6 (ie 12%2F2=6)
Now square 6 to get 36 (ie %286%29%5E2=36)



x%5E2%2B12x%2B36=-13%2B36 Add this result (36) to both sides. Now the expression x%5E2%2B12x%2B36 is a perfect square trinomial.




%28x%2B6%29%5E2=-13%2B36 Factor x%5E2%2B12x%2B36 into %28x%2B6%29%5E2 (note: if you need help with factoring, check out this solver)



%28x%2B6%29%5E2=23 Combine like terms on the right side

x%2B6=0%2B-sqrt%2823%29 Take the square root of both sides

x=-6%2B-sqrt%2823%29 Subtract 6 from both sides to isolate x.

So the expression breaks down to
x=-6%2Bsqrt%2823%29 or x=-6-sqrt%2823%29


So our answer is approximately
x=-1.20416847668728 or x=-10.7958315233127

Here is visual proof

+graph%28+500%2C+500%2C+-12%2C+10%2C+-10%2C+10%2C+x%5E2%2B12x%2B13%29+ graph of y=x%5E2%2B12x%2B13


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.