0=4x^2-120x-400

Solution for 0=4x^2-120x-400 equation:

Simplifying
0 = 4x2 + -120x + -400

Reorder the terms:
0 = -400 + -120x + 4x2

Solving
0 = -400 + -120x + 4x2

Solving for variable 'x'.

Combine like terms: 0 + 400 = 400
400 + 120x + -4x2 = -400 + -120x + 4x2 + 400 + 120x + -4x2

Reorder the terms:
400 + 120x + -4x2 = -400 + 400 + -120x + 120x + 4x2 + -4x2

Combine like terms: -400 + 400 = 0
400 + 120x + -4x2 = 0 + -120x + 120x + 4x2 + -4x2
400 + 120x + -4x2 = -120x + 120x + 4x2 + -4x2

Combine like terms: -120x + 120x = 0
400 + 120x + -4x2 = 0 + 4x2 + -4x2
400 + 120x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
400 + 120x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(100 + 30x + -1x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(100 + 30x + -1x2)' equal to zero and attempt to solve:

Simplifying
100 + 30x + -1x2 = 0

Solving
100 + 30x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-100 + -30x + x2 = 0

Move the constant term to the right:

Add '100' to each side of the equation.
-100 + -30x + 100 + x2 = 0 + 100

Reorder the terms:
-100 + 100 + -30x + x2 = 0 + 100

Combine like terms: -100 + 100 = 0
0 + -30x + x2 = 0 + 100
-30x + x2 = 0 + 100

Combine like terms: 0 + 100 = 100
-30x + x2 = 100

The x term is -30x.  Take half its coefficient (-15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
-30x + 225 + x2 = 100 + 225

Reorder the terms:
225 + -30x + x2 = 100 + 225

Combine like terms: 100 + 225 = 325
225 + -30x + x2 = 325

Factor a perfect square on the left side:
(x + -15)(x + -15) = 325

Calculate the square root of the right side: 18.027756377

Break this problem into two subproblems by setting 
(x + -15) equal to 18.027756377 and -18.027756377.

Subproblem 1
x + -15 = 18.027756377

Simplifying
x + -15 = 18.027756377

Reorder the terms:
-15 + x = 18.027756377

Solving
-15 + x = 18.027756377

Solving for variable 'x'.

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

Add '15' to each side of the equation.
-15 + 15 + x = 18.027756377 + 15

Combine like terms: -15 + 15 = 0
0 + x = 18.027756377 + 15
x = 18.027756377 + 15

Combine like terms: 18.027756377 + 15 = 33.027756377
x = 33.027756377

Simplifying
x = 33.027756377

Subproblem 2
x + -15 = -18.027756377

Simplifying
x + -15 = -18.027756377

Reorder the terms:
-15 + x = -18.027756377

Solving
-15 + x = -18.027756377

Solving for variable 'x'.

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

Add '15' to each side of the equation.
-15 + 15 + x = -18.027756377 + 15

Combine like terms: -15 + 15 = 0
0 + x = -18.027756377 + 15
x = -18.027756377 + 15

Combine like terms: -18.027756377 + 15 = -3.027756377
x = -3.027756377

Simplifying
x = -3.027756377

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {33.027756377, -3.027756377}
Solution
x = {33.027756377, -3.027756377}