4x^2-48x-144=0

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Solution for 4x^2-48x-144=0 equation: 


Simplifying
4x2 + -48x + -144 = 0

Reorder the terms:
-144 + -48x + 4x2 = 0

Solving
-144 + -48x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-36 + -12x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-36 + -12x + x2)' equal to zero and attempt to solve:

Simplifying
-36 + -12x + x2 = 0

Solving
-36 + -12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + -12x + 36 + x2 = 0 + 36

Reorder the terms:
-36 + 36 + -12x + x2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + -12x + x2 = 0 + 36
-12x + x2 = 0 + 36

Combine like terms: 0 + 36 = 36
-12x + x2 = 36

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 = 36 + 36

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

Combine like terms: 36 + 36 = 72
36 + -12x + x2 = 72

Factor a perfect square on the left side:
(x + -6)(x + -6) = 72

Calculate the square root of the right side: 8.485281374

Break this problem into two subproblems by setting 
(x + -6) equal to 8.485281374 and -8.485281374.


Subproblem 1
x + -6 = 8.485281374

Simplifying
x + -6 = 8.485281374

Reorder the terms:
-6 + x = 8.485281374

Solving
-6 + x = 8.485281374

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 = 8.485281374 + 6

Combine like terms: -6 + 6 = 0
0 + x = 8.485281374 + 6
x = 8.485281374 + 6

Combine like terms: 8.485281374 + 6 = 14.485281374
x = 14.485281374

Simplifying
x = 14.485281374


Subproblem 2
x + -6 = -8.485281374

Simplifying
x + -6 = -8.485281374

Reorder the terms:
-6 + x = -8.485281374

Solving
-6 + x = -8.485281374

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 = -8.485281374 + 6

Combine like terms: -6 + 6 = 0
0 + x = -8.485281374 + 6
x = -8.485281374 + 6

Combine like terms: -8.485281374 + 6 = -2.485281374
x = -2.485281374

Simplifying
x = -2.485281374


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.485281374, -2.485281374}
Solution
x = {14.485281374, -2.485281374}

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