4x^2+50x-120=0

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Solution for 4x^2+50x-120=0 equation: 


Simplifying
4x2 + 50x + -120 = 0

Reorder the terms:
-120 + 50x + 4x2 = 0

Solving
-120 + 50x + 4x2 = 0

Solving for variable 'x'.

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

Ignore the factor 2.

Subproblem 1
Set the factor '(-60 + 25x + 2x2)' equal to zero and attempt to solve:

Simplifying
-60 + 25x + 2x2 = 0

Solving
-60 + 25x + 2x2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-30 + 12.5x + x2 = 0

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + 12.5x + 30 + x2 = 0 + 30

Reorder the terms:
-30 + 30 + 12.5x + x2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + 12.5x + x2 = 0 + 30
12.5x + x2 = 0 + 30

Combine like terms: 0 + 30 = 30
12.5x + x2 = 30

The x term is 12.5x.  Take half its coefficient (6.25).
Square it (39.0625) and add it to both sides.

Add '39.0625' to each side of the equation.
12.5x + 39.0625 + x2 = 30 + 39.0625

Reorder the terms:
39.0625 + 12.5x + x2 = 30 + 39.0625

Combine like terms: 30 + 39.0625 = 69.0625
39.0625 + 12.5x + x2 = 69.0625

Factor a perfect square on the left side:
(x + 6.25)(x + 6.25) = 69.0625

Calculate the square root of the right side: 8.310385069

Break this problem into two subproblems by setting 
(x + 6.25) equal to 8.310385069 and -8.310385069.


Subproblem 1
x + 6.25 = 8.310385069

Simplifying
x + 6.25 = 8.310385069

Reorder the terms:
6.25 + x = 8.310385069

Solving
6.25 + x = 8.310385069

Solving for variable 'x'.

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

Add '-6.25' to each side of the equation.
6.25 + -6.25 + x = 8.310385069 + -6.25

Combine like terms: 6.25 + -6.25 = 0.00
0.00 + x = 8.310385069 + -6.25
x = 8.310385069 + -6.25

Combine like terms: 8.310385069 + -6.25 = 2.060385069
x = 2.060385069

Simplifying
x = 2.060385069


Subproblem 2
x + 6.25 = -8.310385069

Simplifying
x + 6.25 = -8.310385069

Reorder the terms:
6.25 + x = -8.310385069

Solving
6.25 + x = -8.310385069

Solving for variable 'x'.

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

Add '-6.25' to each side of the equation.
6.25 + -6.25 + x = -8.310385069 + -6.25

Combine like terms: 6.25 + -6.25 = 0.00
0.00 + x = -8.310385069 + -6.25
x = -8.310385069 + -6.25

Combine like terms: -8.310385069 + -6.25 = -14.560385069
x = -14.560385069

Simplifying
x = -14.560385069


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.060385069, -14.560385069}
Solution
x = {2.060385069, -14.560385069}

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