0=-4x^2+48x+108

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Solution for 0=-4x^2+48x+108 equation: 


Simplifying
0 = -4x2 + 48x + 108

Reorder the terms:
0 = 108 + 48x + -4x2

Solving
0 = 108 + 48x + -4x2

Solving for variable 'x'.

Combine like terms: 0 + -108 = -108
-108 + -48x + 4x2 = 108 + 48x + -4x2 + -108 + -48x + 4x2

Reorder the terms:
-108 + -48x + 4x2 = 108 + -108 + 48x + -48x + -4x2 + 4x2

Combine like terms: 108 + -108 = 0
-108 + -48x + 4x2 = 0 + 48x + -48x + -4x2 + 4x2
-108 + -48x + 4x2 = 48x + -48x + -4x2 + 4x2

Combine like terms: 48x + -48x = 0
-108 + -48x + 4x2 = 0 + -4x2 + 4x2
-108 + -48x + 4x2 = -4x2 + 4x2

Combine like terms: -4x2 + 4x2 = 0
-108 + -48x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-27 + -12x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-27 + -12x + x2)' equal to zero and attempt to solve:

Simplifying
-27 + -12x + x2 = 0

Solving
-27 + -12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '27' to each side of the equation.
-27 + -12x + 27 + x2 = 0 + 27

Reorder the terms:
-27 + 27 + -12x + x2 = 0 + 27

Combine like terms: -27 + 27 = 0
0 + -12x + x2 = 0 + 27
-12x + x2 = 0 + 27

Combine like terms: 0 + 27 = 27
-12x + x2 = 27

The x term is -12x.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12x + 36 + x2 = 27 + 36

Reorder the terms:
36 + -12x + x2 = 27 + 36

Combine like terms: 27 + 36 = 63
36 + -12x + x2 = 63

Factor a perfect square on the left side:
(x + -6)(x + -6) = 63

Calculate the square root of the right side: 7.937253933

Break this problem into two subproblems by setting 
(x + -6) equal to 7.937253933 and -7.937253933.


Subproblem 1
x + -6 = 7.937253933

Simplifying
x + -6 = 7.937253933

Reorder the terms:
-6 + x = 7.937253933

Solving
-6 + x = 7.937253933

Solving for variable 'x'.

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

Add '6' to each side of the equation.
-6 + 6 + x = 7.937253933 + 6

Combine like terms: -6 + 6 = 0
0 + x = 7.937253933 + 6
x = 7.937253933 + 6

Combine like terms: 7.937253933 + 6 = 13.937253933
x = 13.937253933

Simplifying
x = 13.937253933


Subproblem 2
x + -6 = -7.937253933

Simplifying
x + -6 = -7.937253933

Reorder the terms:
-6 + x = -7.937253933

Solving
-6 + x = -7.937253933

Solving for variable 'x'.

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

Add '6' to each side of the equation.
-6 + 6 + x = -7.937253933 + 6

Combine like terms: -6 + 6 = 0
0 + x = -7.937253933 + 6
x = -7.937253933 + 6

Combine like terms: -7.937253933 + 6 = -1.937253933
x = -1.937253933

Simplifying
x = -1.937253933


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.937253933, -1.937253933}
Solution
x = {13.937253933, -1.937253933}

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