x^2+10*x-125=0

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Solution for x^2+10*x-125=0 equation:


Simplifying
x2 + 10x + -125 = 0

Reorder the terms:
-125 + 10x + x2 = 0

Solving
-125 + 10x + 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 + 10x + 125 + x2 = 0 + 125

Reorder the terms:
-125 + 125 + 10x + x2 = 0 + 125

Combine like terms: -125 + 125 = 0
0 + 10x + x2 = 0 + 125
10x + x2 = 0 + 125

Combine like terms: 0 + 125 = 125
10x + x2 = 125

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 = 125 + 25

Reorder the terms:
25 + 10x + x2 = 125 + 25

Combine like terms: 125 + 25 = 150
25 + 10x + x2 = 150

Factor a perfect square on the left side:
(x + 5)(x + 5) = 150

Calculate the square root of the right side: 12.247448714

Break this problem into two subproblems by setting 
(x + 5) equal to 12.247448714 and -12.247448714.

Subproblem 1

x + 5 = 12.247448714 Simplifying x + 5 = 12.247448714 Reorder the terms: 5 + x = 12.247448714 Solving 5 + x = 12.247448714 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 = 12.247448714 + -5 Combine like terms: 5 + -5 = 0 0 + x = 12.247448714 + -5 x = 12.247448714 + -5 Combine like terms: 12.247448714 + -5 = 7.247448714 x = 7.247448714 Simplifying x = 7.247448714

Subproblem 2

x + 5 = -12.247448714 Simplifying x + 5 = -12.247448714 Reorder the terms: 5 + x = -12.247448714 Solving 5 + x = -12.247448714 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 = -12.247448714 + -5 Combine like terms: 5 + -5 = 0 0 + x = -12.247448714 + -5 x = -12.247448714 + -5 Combine like terms: -12.247448714 + -5 = -17.247448714 x = -17.247448714 Simplifying x = -17.247448714

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.247448714, -17.247448714}

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