x^2+32x+113=0

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Solution for x^2+32x+113=0 equation:


Simplifying
x2 + 32x + 113 = 0

Reorder the terms:
113 + 32x + x2 = 0

Solving
113 + 32x + 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 + 32x + -113 + x2 = 0 + -113

Reorder the terms:
113 + -113 + 32x + x2 = 0 + -113

Combine like terms: 113 + -113 = 0
0 + 32x + x2 = 0 + -113
32x + x2 = 0 + -113

Combine like terms: 0 + -113 = -113
32x + x2 = -113

The x term is 32x.  Take half its coefficient (16).
Square it (256) and add it to both sides.

Add '256' to each side of the equation.
32x + 256 + x2 = -113 + 256

Reorder the terms:
256 + 32x + x2 = -113 + 256

Combine like terms: -113 + 256 = 143
256 + 32x + x2 = 143

Factor a perfect square on the left side:
(x + 16)(x + 16) = 143

Calculate the square root of the right side: 11.958260743

Break this problem into two subproblems by setting 
(x + 16) equal to 11.958260743 and -11.958260743.

Subproblem 1

x + 16 = 11.958260743 Simplifying x + 16 = 11.958260743 Reorder the terms: 16 + x = 11.958260743 Solving 16 + x = 11.958260743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x = 11.958260743 + -16 Combine like terms: 16 + -16 = 0 0 + x = 11.958260743 + -16 x = 11.958260743 + -16 Combine like terms: 11.958260743 + -16 = -4.041739257 x = -4.041739257 Simplifying x = -4.041739257

Subproblem 2

x + 16 = -11.958260743 Simplifying x + 16 = -11.958260743 Reorder the terms: 16 + x = -11.958260743 Solving 16 + x = -11.958260743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x = -11.958260743 + -16 Combine like terms: 16 + -16 = 0 0 + x = -11.958260743 + -16 x = -11.958260743 + -16 Combine like terms: -11.958260743 + -16 = -27.958260743 x = -27.958260743 Simplifying x = -27.958260743

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-4.041739257, -27.958260743}

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