x^2+16x-113=0

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Solution for x^2+16x-113=0 equation:


Simplifying
x2 + 16x + -113 = 0

Reorder the terms:
-113 + 16x + x2 = 0

Solving
-113 + 16x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '113' to each side of the equation.
-113 + 16x + 113 + x2 = 0 + 113

Reorder the terms:
-113 + 113 + 16x + x2 = 0 + 113

Combine like terms: -113 + 113 = 0
0 + 16x + x2 = 0 + 113
16x + x2 = 0 + 113

Combine like terms: 0 + 113 = 113
16x + x2 = 113

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 = 113 + 64

Reorder the terms:
64 + 16x + x2 = 113 + 64

Combine like terms: 113 + 64 = 177
64 + 16x + x2 = 177

Factor a perfect square on the left side:
(x + 8)(x + 8) = 177

Calculate the square root of the right side: 13.304134696

Break this problem into two subproblems by setting 
(x + 8) equal to 13.304134696 and -13.304134696.

Subproblem 1

x + 8 = 13.304134696 Simplifying x + 8 = 13.304134696 Reorder the terms: 8 + x = 13.304134696 Solving 8 + x = 13.304134696 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 = 13.304134696 + -8 Combine like terms: 8 + -8 = 0 0 + x = 13.304134696 + -8 x = 13.304134696 + -8 Combine like terms: 13.304134696 + -8 = 5.304134696 x = 5.304134696 Simplifying x = 5.304134696

Subproblem 2

x + 8 = -13.304134696 Simplifying x + 8 = -13.304134696 Reorder the terms: 8 + x = -13.304134696 Solving 8 + x = -13.304134696 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 = -13.304134696 + -8 Combine like terms: 8 + -8 = 0 0 + x = -13.304134696 + -8 x = -13.304134696 + -8 Combine like terms: -13.304134696 + -8 = -21.304134696 x = -21.304134696 Simplifying x = -21.304134696

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.304134696, -21.304134696}

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