x^2-5x-120=0

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Solution for x^2-5x-120=0 equation: 


Simplifying
x2 + -5x + -120 = 0

Reorder the terms:
-120 + -5x + x2 = 0

Solving
-120 + -5x + 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 + -5x + 120 + x2 = 0 + 120

Reorder the terms:
-120 + 120 + -5x + x2 = 0 + 120

Combine like terms: -120 + 120 = 0
0 + -5x + x2 = 0 + 120
-5x + x2 = 0 + 120

Combine like terms: 0 + 120 = 120
-5x + x2 = 120

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 120 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 120 + 6.25

Combine like terms: 120 + 6.25 = 126.25
6.25 + -5x + x2 = 126.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 126.25

Calculate the square root of the right side: 11.236102527

Break this problem into two subproblems by setting 
(x + -2.5) equal to 11.236102527 and -11.236102527.


Subproblem 1
x + -2.5 = 11.236102527

Simplifying
x + -2.5 = 11.236102527

Reorder the terms:
-2.5 + x = 11.236102527

Solving
-2.5 + x = 11.236102527

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 11.236102527 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 11.236102527 + 2.5
x = 11.236102527 + 2.5

Combine like terms: 11.236102527 + 2.5 = 13.736102527
x = 13.736102527

Simplifying
x = 13.736102527


Subproblem 2
x + -2.5 = -11.236102527

Simplifying
x + -2.5 = -11.236102527

Reorder the terms:
-2.5 + x = -11.236102527

Solving
-2.5 + x = -11.236102527

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -11.236102527 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -11.236102527 + 2.5
x = -11.236102527 + 2.5

Combine like terms: -11.236102527 + 2.5 = -8.736102527
x = -8.736102527

Simplifying
x = -8.736102527


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.736102527, -8.736102527}

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