4x^2+68x-120=0

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Solution for 4x^2+68x-120=0 equation: 


Simplifying
4x2 + 68x + -120 = 0

Reorder the terms:
-120 + 68x + 4x2 = 0

Solving
-120 + 68x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-30 + 17x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-30 + 17x + x2)' equal to zero and attempt to solve:

Simplifying
-30 + 17x + x2 = 0

Solving
-30 + 17x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + 17x + 30 + x2 = 0 + 30

Reorder the terms:
-30 + 30 + 17x + x2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + 17x + x2 = 0 + 30
17x + x2 = 0 + 30

Combine like terms: 0 + 30 = 30
17x + x2 = 30

The x term is 17x.  Take half its coefficient (8.5).
Square it (72.25) and add it to both sides.

Add '72.25' to each side of the equation.
17x + 72.25 + x2 = 30 + 72.25

Reorder the terms:
72.25 + 17x + x2 = 30 + 72.25

Combine like terms: 30 + 72.25 = 102.25
72.25 + 17x + x2 = 102.25

Factor a perfect square on the left side:
(x + 8.5)(x + 8.5) = 102.25

Calculate the square root of the right side: 10.111874208

Break this problem into two subproblems by setting 
(x + 8.5) equal to 10.111874208 and -10.111874208.


Subproblem 1
x + 8.5 = 10.111874208

Simplifying
x + 8.5 = 10.111874208

Reorder the terms:
8.5 + x = 10.111874208

Solving
8.5 + x = 10.111874208

Solving for variable 'x'.

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

Add '-8.5' to each side of the equation.
8.5 + -8.5 + x = 10.111874208 + -8.5

Combine like terms: 8.5 + -8.5 = 0.0
0.0 + x = 10.111874208 + -8.5
x = 10.111874208 + -8.5

Combine like terms: 10.111874208 + -8.5 = 1.611874208
x = 1.611874208

Simplifying
x = 1.611874208


Subproblem 2
x + 8.5 = -10.111874208

Simplifying
x + 8.5 = -10.111874208

Reorder the terms:
8.5 + x = -10.111874208

Solving
8.5 + x = -10.111874208

Solving for variable 'x'.

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

Add '-8.5' to each side of the equation.
8.5 + -8.5 + x = -10.111874208 + -8.5

Combine like terms: 8.5 + -8.5 = 0.0
0.0 + x = -10.111874208 + -8.5
x = -10.111874208 + -8.5

Combine like terms: -10.111874208 + -8.5 = -18.611874208
x = -18.611874208

Simplifying
x = -18.611874208


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.611874208, -18.611874208}
Solution
x = {1.611874208, -18.611874208}

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