4x^2-96x+192=0

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Solution for 4x^2-96x+192=0 equation: 


Simplifying
4x2 + -96x + 192 = 0

Reorder the terms:
192 + -96x + 4x2 = 0

Solving
192 + -96x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(48 + -24x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(48 + -24x + x2)' equal to zero and attempt to solve:

Simplifying
48 + -24x + x2 = 0

Solving
48 + -24x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-48' to each side of the equation.
48 + -24x + -48 + x2 = 0 + -48

Reorder the terms:
48 + -48 + -24x + x2 = 0 + -48

Combine like terms: 48 + -48 = 0
0 + -24x + x2 = 0 + -48
-24x + x2 = 0 + -48

Combine like terms: 0 + -48 = -48
-24x + x2 = -48

The x term is -24x.  Take half its coefficient (-12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
-24x + 144 + x2 = -48 + 144

Reorder the terms:
144 + -24x + x2 = -48 + 144

Combine like terms: -48 + 144 = 96
144 + -24x + x2 = 96

Factor a perfect square on the left side:
(x + -12)(x + -12) = 96

Calculate the square root of the right side: 9.797958971

Break this problem into two subproblems by setting 
(x + -12) equal to 9.797958971 and -9.797958971.


Subproblem 1
x + -12 = 9.797958971

Simplifying
x + -12 = 9.797958971

Reorder the terms:
-12 + x = 9.797958971

Solving
-12 + x = 9.797958971

Solving for variable 'x'.

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

Add '12' to each side of the equation.
-12 + 12 + x = 9.797958971 + 12

Combine like terms: -12 + 12 = 0
0 + x = 9.797958971 + 12
x = 9.797958971 + 12

Combine like terms: 9.797958971 + 12 = 21.797958971
x = 21.797958971

Simplifying
x = 21.797958971


Subproblem 2
x + -12 = -9.797958971

Simplifying
x + -12 = -9.797958971

Reorder the terms:
-12 + x = -9.797958971

Solving
-12 + x = -9.797958971

Solving for variable 'x'.

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

Add '12' to each side of the equation.
-12 + 12 + x = -9.797958971 + 12

Combine like terms: -12 + 12 = 0
0 + x = -9.797958971 + 12
x = -9.797958971 + 12

Combine like terms: -9.797958971 + 12 = 2.202041029
x = 2.202041029

Simplifying
x = 2.202041029


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {21.797958971, 2.202041029}
Solution
x = {21.797958971, 2.202041029}

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