2x^2-50x-120=0

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Solution for 2x^2-50x-120=0 equation: 


Simplifying
2x2 + -50x + -120 = 0

Reorder the terms:
-120 + -50x + 2x2 = 0

Solving
-120 + -50x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-60 + -25x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-60 + -25x + x2)' equal to zero and attempt to solve:

Simplifying
-60 + -25x + x2 = 0

Solving
-60 + -25x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '60' to each side of the equation.
-60 + -25x + 60 + x2 = 0 + 60

Reorder the terms:
-60 + 60 + -25x + x2 = 0 + 60

Combine like terms: -60 + 60 = 0
0 + -25x + x2 = 0 + 60
-25x + x2 = 0 + 60

Combine like terms: 0 + 60 = 60
-25x + x2 = 60

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 = 60 + 156.25

Reorder the terms:
156.25 + -25x + x2 = 60 + 156.25

Combine like terms: 60 + 156.25 = 216.25
156.25 + -25x + x2 = 216.25

Factor a perfect square on the left side:
(x + -12.5)(x + -12.5) = 216.25

Calculate the square root of the right side: 14.70544117

Break this problem into two subproblems by setting 
(x + -12.5) equal to 14.70544117 and -14.70544117.


Subproblem 1
x + -12.5 = 14.70544117

Simplifying
x + -12.5 = 14.70544117

Reorder the terms:
-12.5 + x = 14.70544117

Solving
-12.5 + x = 14.70544117

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 = 14.70544117 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + x = 14.70544117 + 12.5
x = 14.70544117 + 12.5

Combine like terms: 14.70544117 + 12.5 = 27.20544117
x = 27.20544117

Simplifying
x = 27.20544117


Subproblem 2
x + -12.5 = -14.70544117

Simplifying
x + -12.5 = -14.70544117

Reorder the terms:
-12.5 + x = -14.70544117

Solving
-12.5 + x = -14.70544117

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 = -14.70544117 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + x = -14.70544117 + 12.5
x = -14.70544117 + 12.5

Combine like terms: -14.70544117 + 12.5 = -2.20544117
x = -2.20544117

Simplifying
x = -2.20544117


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {27.20544117, -2.20544117}
Solution
x = {27.20544117, -2.20544117}

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