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

Question 100957: Solve the equation by completing the square
x^2 + 15 = -10x
Found 2 solutions by edjones, jim_thompson5910:
Answer by edjones(8007) (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) (Show Source): You can put this solution on YOUR website!
Start with the given equation

Add 10x to both sides

Subtract 15 from both sides

Take half of the x coefficient 10 to get 5 (ie )
Now square 5 to get 25 (ie )

Add this result (25) to both sides. Now the expression is a perfect square trinomial.

Factor into (note: if you need help with factoring, check out this solver)

Combine like terms on the right side

Take the square root of both sides

Subtract 5 from both sides to isolate x.

So the expression breaks down to
or

So our answer is approximately
or

Here is visual proof

graph of

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

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