x^2+25x-120=0

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Solution for x^2+25x-120=0 equation:


Simplifying
x2 + 25x + -120 = 0

Reorder the terms:
-120 + 25x + x2 = 0

Solving
-120 + 25x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '120' to each side of the equation.
-120 + 25x + 120 + x2 = 0 + 120

Reorder the terms:
-120 + 120 + 25x + x2 = 0 + 120

Combine like terms: -120 + 120 = 0
0 + 25x + x2 = 0 + 120
25x + x2 = 0 + 120

Combine like terms: 0 + 120 = 120
25x + x2 = 120

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 = 120 + 156.25

Reorder the terms:
156.25 + 25x + x2 = 120 + 156.25

Combine like terms: 120 + 156.25 = 276.25
156.25 + 25x + x2 = 276.25

Factor a perfect square on the left side:
(x + 12.5)(x + 12.5) = 276.25

Calculate the square root of the right side: 16.620770139

Break this problem into two subproblems by setting 
(x + 12.5) equal to 16.620770139 and -16.620770139.

Subproblem 1

x + 12.5 = 16.620770139 Simplifying x + 12.5 = 16.620770139 Reorder the terms: 12.5 + x = 16.620770139 Solving 12.5 + x = 16.620770139 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 = 16.620770139 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = 16.620770139 + -12.5 x = 16.620770139 + -12.5 Combine like terms: 16.620770139 + -12.5 = 4.120770139 x = 4.120770139 Simplifying x = 4.120770139

Subproblem 2

x + 12.5 = -16.620770139 Simplifying x + 12.5 = -16.620770139 Reorder the terms: 12.5 + x = -16.620770139 Solving 12.5 + x = -16.620770139 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 = -16.620770139 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = -16.620770139 + -12.5 x = -16.620770139 + -12.5 Combine like terms: -16.620770139 + -12.5 = -29.120770139 x = -29.120770139 Simplifying x = -29.120770139

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.120770139, -29.120770139}

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