x^2+8x-125=0

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Solution for x^2+8x-125=0 equation:


Simplifying
x2 + 8x + -125 = 0

Reorder the terms:
-125 + 8x + x2 = 0

Solving
-125 + 8x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '125' to each side of the equation.
-125 + 8x + 125 + x2 = 0 + 125

Reorder the terms:
-125 + 125 + 8x + x2 = 0 + 125

Combine like terms: -125 + 125 = 0
0 + 8x + x2 = 0 + 125
8x + x2 = 0 + 125

Combine like terms: 0 + 125 = 125
8x + x2 = 125

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = 125 + 16

Reorder the terms:
16 + 8x + x2 = 125 + 16

Combine like terms: 125 + 16 = 141
16 + 8x + x2 = 141

Factor a perfect square on the left side:
(x + 4)(x + 4) = 141

Calculate the square root of the right side: 11.874342087

Break this problem into two subproblems by setting 
(x + 4) equal to 11.874342087 and -11.874342087.

Subproblem 1

x + 4 = 11.874342087 Simplifying x + 4 = 11.874342087 Reorder the terms: 4 + x = 11.874342087 Solving 4 + x = 11.874342087 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 11.874342087 + -4 Combine like terms: 4 + -4 = 0 0 + x = 11.874342087 + -4 x = 11.874342087 + -4 Combine like terms: 11.874342087 + -4 = 7.874342087 x = 7.874342087 Simplifying x = 7.874342087

Subproblem 2

x + 4 = -11.874342087 Simplifying x + 4 = -11.874342087 Reorder the terms: 4 + x = -11.874342087 Solving 4 + x = -11.874342087 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -11.874342087 + -4 Combine like terms: 4 + -4 = 0 0 + x = -11.874342087 + -4 x = -11.874342087 + -4 Combine like terms: -11.874342087 + -4 = -15.874342087 x = -15.874342087 Simplifying x = -15.874342087

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.874342087, -15.874342087}

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