4x^2=4(x+120)

Solution for 4x^2=4(x+120) equation:

Simplifying
4x2 = 4(x + 120)

Reorder the terms:
4x2 = 4(120 + x)
4x2 = (120 * 4 + x * 4)
4x2 = (480 + 4x)

Solving
4x2 = 480 + 4x

Solving for variable 'x'.

Reorder the terms:
-480 + -4x + 4x2 = 480 + 4x + -480 + -4x

Reorder the terms:
-480 + -4x + 4x2 = 480 + -480 + 4x + -4x

Combine like terms: 480 + -480 = 0
-480 + -4x + 4x2 = 0 + 4x + -4x
-480 + -4x + 4x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-480 + -4x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-120 + -1x + x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-120 + -1x + x2)' equal to zero and attempt to solve:

Simplifying
-120 + -1x + x2 = 0

Solving
-120 + -1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '120' to each side of the equation.
-120 + -1x + 120 + x2 = 0 + 120

Reorder the terms:
-120 + 120 + -1x + x2 = 0 + 120

Combine like terms: -120 + 120 = 0
0 + -1x + x2 = 0 + 120
-1x + x2 = 0 + 120

Combine like terms: 0 + 120 = 120
-1x + x2 = 120

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 120 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 120 + 0.25

Combine like terms: 120 + 0.25 = 120.25
0.25 + -1x + x2 = 120.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 120.25

Calculate the square root of the right side: 10.9658561

Break this problem into two subproblems by setting 
(x + -0.5) equal to 10.9658561 and -10.9658561.

Subproblem 1
x + -0.5 = 10.9658561

Simplifying
x + -0.5 = 10.9658561

Reorder the terms:
-0.5 + x = 10.9658561

Solving
-0.5 + x = 10.9658561

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = 10.9658561 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 10.9658561 + 0.5
x = 10.9658561 + 0.5

Combine like terms: 10.9658561 + 0.5 = 11.4658561
x = 11.4658561

Simplifying
x = 11.4658561

Subproblem 2
x + -0.5 = -10.9658561

Simplifying
x + -0.5 = -10.9658561

Reorder the terms:
-0.5 + x = -10.9658561

Solving
-0.5 + x = -10.9658561

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = -10.9658561 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -10.9658561 + 0.5
x = -10.9658561 + 0.5

Combine like terms: -10.9658561 + 0.5 = -10.4658561
x = -10.4658561

Simplifying
x = -10.4658561

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.4658561, -10.4658561}
Solution
x = {11.4658561, -10.4658561}