x^2-125x-500=0

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Solution for x^2-125x-500=0 equation:


Simplifying
x2 + -125x + -500 = 0

Reorder the terms:
-500 + -125x + x2 = 0

Solving
-500 + -125x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '500' to each side of the equation.
-500 + -125x + 500 + x2 = 0 + 500

Reorder the terms:
-500 + 500 + -125x + x2 = 0 + 500

Combine like terms: -500 + 500 = 0
0 + -125x + x2 = 0 + 500
-125x + x2 = 0 + 500

Combine like terms: 0 + 500 = 500
-125x + x2 = 500

The x term is -125x.  Take half its coefficient (-62.5).
Square it (3906.25) and add it to both sides.

Add '3906.25' to each side of the equation.
-125x + 3906.25 + x2 = 500 + 3906.25

Reorder the terms:
3906.25 + -125x + x2 = 500 + 3906.25

Combine like terms: 500 + 3906.25 = 4406.25
3906.25 + -125x + x2 = 4406.25

Factor a perfect square on the left side:
(x + -62.5)(x + -62.5) = 4406.25

Calculate the square root of the right side: 66.379590237

Break this problem into two subproblems by setting 
(x + -62.5) equal to 66.379590237 and -66.379590237.

Subproblem 1

x + -62.5 = 66.379590237 Simplifying x + -62.5 = 66.379590237 Reorder the terms: -62.5 + x = 66.379590237 Solving -62.5 + x = 66.379590237 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '62.5' to each side of the equation. -62.5 + 62.5 + x = 66.379590237 + 62.5 Combine like terms: -62.5 + 62.5 = 0.0 0.0 + x = 66.379590237 + 62.5 x = 66.379590237 + 62.5 Combine like terms: 66.379590237 + 62.5 = 128.879590237 x = 128.879590237 Simplifying x = 128.879590237

Subproblem 2

x + -62.5 = -66.379590237 Simplifying x + -62.5 = -66.379590237 Reorder the terms: -62.5 + x = -66.379590237 Solving -62.5 + x = -66.379590237 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '62.5' to each side of the equation. -62.5 + 62.5 + x = -66.379590237 + 62.5 Combine like terms: -62.5 + 62.5 = 0.0 0.0 + x = -66.379590237 + 62.5 x = -66.379590237 + 62.5 Combine like terms: -66.379590237 + 62.5 = -3.879590237 x = -3.879590237 Simplifying x = -3.879590237

Solution

The solution to the problem is based on the solutions from the subproblems. x = {128.879590237, -3.879590237}

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