x^2+10x+15=0

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Solution for x^2+10x+15=0 equation: 


Simplifying
x2 + 10x + 15 = 0

Reorder the terms:
15 + 10x + x2 = 0

Solving
15 + 10x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-15' to each side of the equation.
15 + 10x + -15 + x2 = 0 + -15

Reorder the terms:
15 + -15 + 10x + x2 = 0 + -15

Combine like terms: 15 + -15 = 0
0 + 10x + x2 = 0 + -15
10x + x2 = 0 + -15

Combine like terms: 0 + -15 = -15
10x + x2 = -15

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = -15 + 25

Reorder the terms:
25 + 10x + x2 = -15 + 25

Combine like terms: -15 + 25 = 10
25 + 10x + x2 = 10

Factor a perfect square on the left side:
(x + 5)(x + 5) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(x + 5) equal to 3.16227766 and -3.16227766.


Subproblem 1
x + 5 = 3.16227766

Simplifying
x + 5 = 3.16227766

Reorder the terms:
5 + x = 3.16227766

Solving
5 + x = 3.16227766

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + x = 3.16227766 + -5

Combine like terms: 5 + -5 = 0
0 + x = 3.16227766 + -5
x = 3.16227766 + -5

Combine like terms: 3.16227766 + -5 = -1.83772234
x = -1.83772234

Simplifying
x = -1.83772234


Subproblem 2
x + 5 = -3.16227766

Simplifying
x + 5 = -3.16227766

Reorder the terms:
5 + x = -3.16227766

Solving
5 + x = -3.16227766

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + x = -3.16227766 + -5

Combine like terms: 5 + -5 = 0
0 + x = -3.16227766 + -5
x = -3.16227766 + -5

Combine like terms: -3.16227766 + -5 = -8.16227766
x = -8.16227766

Simplifying
x = -8.16227766


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.83772234, -8.16227766}

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