x^2-25x-460=0

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Solution for x^2-25x-460=0 equation:


Simplifying
x2 + -25x + -460 = 0

Reorder the terms:
-460 + -25x + x2 = 0

Solving
-460 + -25x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '460' to each side of the equation.
-460 + -25x + 460 + x2 = 0 + 460

Reorder the terms:
-460 + 460 + -25x + x2 = 0 + 460

Combine like terms: -460 + 460 = 0
0 + -25x + x2 = 0 + 460
-25x + x2 = 0 + 460

Combine like terms: 0 + 460 = 460
-25x + x2 = 460

The x term is -25x.  Take half its coefficient (-12.5).
Square it (156.25) and add it to both sides.

Add '156.25' to each side of the equation.
-25x + 156.25 + x2 = 460 + 156.25

Reorder the terms:
156.25 + -25x + x2 = 460 + 156.25

Combine like terms: 460 + 156.25 = 616.25
156.25 + -25x + x2 = 616.25

Factor a perfect square on the left side:
(x + -12.5)(x + -12.5) = 616.25

Calculate the square root of the right side: 24.824383175

Break this problem into two subproblems by setting 
(x + -12.5) equal to 24.824383175 and -24.824383175.

Subproblem 1

x + -12.5 = 24.824383175 Simplifying x + -12.5 = 24.824383175 Reorder the terms: -12.5 + x = 24.824383175 Solving -12.5 + x = 24.824383175 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = 24.824383175 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = 24.824383175 + 12.5 x = 24.824383175 + 12.5 Combine like terms: 24.824383175 + 12.5 = 37.324383175 x = 37.324383175 Simplifying x = 37.324383175

Subproblem 2

x + -12.5 = -24.824383175 Simplifying x + -12.5 = -24.824383175 Reorder the terms: -12.5 + x = -24.824383175 Solving -12.5 + x = -24.824383175 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = -24.824383175 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = -24.824383175 + 12.5 x = -24.824383175 + 12.5 Combine like terms: -24.824383175 + 12.5 = -12.324383175 x = -12.324383175 Simplifying x = -12.324383175

Solution

The solution to the problem is based on the solutions from the subproblems. x = {37.324383175, -12.324383175}

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