24x^2-96x-92=0

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Solution for 24x^2-96x-92=0 equation: 


Simplifying
24x2 + -96x + -92 = 0

Reorder the terms:
-92 + -96x + 24x2 = 0

Solving
-92 + -96x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-23 + -24x + 6x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-23 + -24x + 6x2)' equal to zero and attempt to solve:

Simplifying
-23 + -24x + 6x2 = 0

Solving
-23 + -24x + 6x2 = 0

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

Divide each side by '6'.
-3.833333333 + -4x + x2 = 0

Move the constant term to the right:

Add '3.833333333' to each side of the equation.
-3.833333333 + -4x + 3.833333333 + x2 = 0 + 3.833333333

Reorder the terms:
-3.833333333 + 3.833333333 + -4x + x2 = 0 + 3.833333333

Combine like terms: -3.833333333 + 3.833333333 = 0.000000000
0.000000000 + -4x + x2 = 0 + 3.833333333
-4x + x2 = 0 + 3.833333333

Combine like terms: 0 + 3.833333333 = 3.833333333
-4x + x2 = 3.833333333

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 3.833333333 + 4

Reorder the terms:
4 + -4x + x2 = 3.833333333 + 4

Combine like terms: 3.833333333 + 4 = 7.833333333
4 + -4x + x2 = 7.833333333

Factor a perfect square on the left side:
(x + -2)(x + -2) = 7.833333333

Calculate the square root of the right side: 2.798809271

Break this problem into two subproblems by setting 
(x + -2) equal to 2.798809271 and -2.798809271.


Subproblem 1
x + -2 = 2.798809271

Simplifying
x + -2 = 2.798809271

Reorder the terms:
-2 + x = 2.798809271

Solving
-2 + x = 2.798809271

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 2.798809271 + 2

Combine like terms: -2 + 2 = 0
0 + x = 2.798809271 + 2
x = 2.798809271 + 2

Combine like terms: 2.798809271 + 2 = 4.798809271
x = 4.798809271

Simplifying
x = 4.798809271


Subproblem 2
x + -2 = -2.798809271

Simplifying
x + -2 = -2.798809271

Reorder the terms:
-2 + x = -2.798809271

Solving
-2 + x = -2.798809271

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -2.798809271 + 2

Combine like terms: -2 + 2 = 0
0 + x = -2.798809271 + 2
x = -2.798809271 + 2

Combine like terms: -2.798809271 + 2 = -0.798809271
x = -0.798809271

Simplifying
x = -0.798809271


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.798809271, -0.798809271}
Solution
x = {4.798809271, -0.798809271}

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