SOLUTION: Solve the equation by completing the square x^2 + 15 = -10x

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Question 100957: Solve the equation by completing the square
x^2 + 15 = -10x
Found 2 solutions by edjones, jim_thompson5910:
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
x^2 + 15 = -10x
x^2+10x+15=0 make equation = 0
x^2+10x=-15 put the constant on the right side.
x^2+10x+25=-15+25 divide the coefficient of x in half and square it to get the new constant and add it to both sides.
(x+5)^2=10 factor the left side.
x+5=+-sqrt(10) get sqrt of both sides.
x= -5+sqrt(10), -5-sqrt(10)
Ed

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2+%2B+15+=+-10x Start with the given equation


x%5E2+%2B10x+%2B+15+=0 Add 10x to both sides




x%5E2%2B10x=-15 Subtract 15 from both sides


Take half of the x coefficient 10 to get 5 (ie 10%2F2=5)
Now square 5 to get 25 (ie %285%29%5E2=25)



x%5E2%2B10x%2B25=-15%2B25 Add this result (25) to both sides. Now the expression x%5E2%2B10x%2B25 is a perfect square trinomial.




%28x%2B5%29%5E2=-15%2B25 Factor x%5E2%2B10x%2B25 into %28x%2B5%29%5E2 (note: if you need help with factoring, check out this solver)



%28x%2B5%29%5E2=10 Combine like terms on the right side

x%2B5=0%2B-sqrt%2810%29 Take the square root of both sides

x=-5%2B-sqrt%2810%29 Subtract 5 from both sides to isolate x.

So the expression breaks down to
x=-5%2Bsqrt%2810%29 or x=-5-sqrt%2810%29


So our answer is approximately
x=-1.83772233983162 or x=-8.16227766016838

Here is visual proof

+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2%2B10x%2B15%29+ graph of y=x%5E2%2B10x%2B15


When we use the root finder feature on a calculator, we would find that the x-intercepts are x=-1.83772233983162 and x=-8.16227766016838, so this verifies our answer.