x^2+16x-15=-8

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Solution for x^2+16x-15=-8 equation: 


Simplifying
x2 + 16x + -15 = -8

Reorder the terms:
-15 + 16x + x2 = -8

Solving
-15 + 16x + x2 = -8

Solving for variable 'x'.

Reorder the terms:
-15 + 8 + 16x + x2 = -8 + 8

Combine like terms: -15 + 8 = -7
-7 + 16x + x2 = -8 + 8

Combine like terms: -8 + 8 = 0
-7 + 16x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + 16x + 7 + x2 = 0 + 7

Reorder the terms:
-7 + 7 + 16x + x2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 16x + x2 = 0 + 7
16x + x2 = 0 + 7

Combine like terms: 0 + 7 = 7
16x + x2 = 7

The x term is 16x.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16x + 64 + x2 = 7 + 64

Reorder the terms:
64 + 16x + x2 = 7 + 64

Combine like terms: 7 + 64 = 71
64 + 16x + x2 = 71

Factor a perfect square on the left side:
(x + 8)(x + 8) = 71

Calculate the square root of the right side: 8.426149773

Break this problem into two subproblems by setting 
(x + 8) equal to 8.426149773 and -8.426149773.


Subproblem 1
x + 8 = 8.426149773

Simplifying
x + 8 = 8.426149773

Reorder the terms:
8 + x = 8.426149773

Solving
8 + x = 8.426149773

Solving for variable 'x'.

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

Add '-8' to each side of the equation.
8 + -8 + x = 8.426149773 + -8

Combine like terms: 8 + -8 = 0
0 + x = 8.426149773 + -8
x = 8.426149773 + -8

Combine like terms: 8.426149773 + -8 = 0.426149773
x = 0.426149773

Simplifying
x = 0.426149773


Subproblem 2
x + 8 = -8.426149773

Simplifying
x + 8 = -8.426149773

Reorder the terms:
8 + x = -8.426149773

Solving
8 + x = -8.426149773

Solving for variable 'x'.

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

Add '-8' to each side of the equation.
8 + -8 + x = -8.426149773 + -8

Combine like terms: 8 + -8 = 0
0 + x = -8.426149773 + -8
x = -8.426149773 + -8

Combine like terms: -8.426149773 + -8 = -16.426149773
x = -16.426149773

Simplifying
x = -16.426149773


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.426149773, -16.426149773}

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