4x^2+80x+120=0

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Solution for 4x^2+80x+120=0 equation: 


Simplifying
4x2 + 80x + 120 = 0

Reorder the terms:
120 + 80x + 4x2 = 0

Solving
120 + 80x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(30 + 20x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(30 + 20x + x2)' equal to zero and attempt to solve:

Simplifying
30 + 20x + x2 = 0

Solving
30 + 20x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-30' to each side of the equation.
30 + 20x + -30 + x2 = 0 + -30

Reorder the terms:
30 + -30 + 20x + x2 = 0 + -30

Combine like terms: 30 + -30 = 0
0 + 20x + x2 = 0 + -30
20x + x2 = 0 + -30

Combine like terms: 0 + -30 = -30
20x + x2 = -30

The x term is 20x.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20x + 100 + x2 = -30 + 100

Reorder the terms:
100 + 20x + x2 = -30 + 100

Combine like terms: -30 + 100 = 70
100 + 20x + x2 = 70

Factor a perfect square on the left side:
(x + 10)(x + 10) = 70

Calculate the square root of the right side: 8.366600265

Break this problem into two subproblems by setting 
(x + 10) equal to 8.366600265 and -8.366600265.


Subproblem 1
x + 10 = 8.366600265

Simplifying
x + 10 = 8.366600265

Reorder the terms:
10 + x = 8.366600265

Solving
10 + x = 8.366600265

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = 8.366600265 + -10

Combine like terms: 10 + -10 = 0
0 + x = 8.366600265 + -10
x = 8.366600265 + -10

Combine like terms: 8.366600265 + -10 = -1.633399735
x = -1.633399735

Simplifying
x = -1.633399735


Subproblem 2
x + 10 = -8.366600265

Simplifying
x + 10 = -8.366600265

Reorder the terms:
10 + x = -8.366600265

Solving
10 + x = -8.366600265

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = -8.366600265 + -10

Combine like terms: 10 + -10 = 0
0 + x = -8.366600265 + -10
x = -8.366600265 + -10

Combine like terms: -8.366600265 + -10 = -18.366600265
x = -18.366600265

Simplifying
x = -18.366600265


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.633399735, -18.366600265}
Solution
x = {-1.633399735, -18.366600265}

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