4x^2-14x-96=0

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Solution for 4x^2-14x-96=0 equation: 


Simplifying
4x2 + -14x + -96 = 0

Reorder the terms:
-96 + -14x + 4x2 = 0

Solving
-96 + -14x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-48 + -7x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-48 + -7x + 2x2)' equal to zero and attempt to solve:

Simplifying
-48 + -7x + 2x2 = 0

Solving
-48 + -7x + 2x2 = 0

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

Divide each side by '2'.
-24 + -3.5x + x2 = 0

Move the constant term to the right:

Add '24' to each side of the equation.
-24 + -3.5x + 24 + x2 = 0 + 24

Reorder the terms:
-24 + 24 + -3.5x + x2 = 0 + 24

Combine like terms: -24 + 24 = 0
0 + -3.5x + x2 = 0 + 24
-3.5x + x2 = 0 + 24

Combine like terms: 0 + 24 = 24
-3.5x + x2 = 24

The x term is -3.5x.  Take half its coefficient (-1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
-3.5x + 3.0625 + x2 = 24 + 3.0625

Reorder the terms:
3.0625 + -3.5x + x2 = 24 + 3.0625

Combine like terms: 24 + 3.0625 = 27.0625
3.0625 + -3.5x + x2 = 27.0625

Factor a perfect square on the left side:
(x + -1.75)(x + -1.75) = 27.0625

Calculate the square root of the right side: 5.202163012

Break this problem into two subproblems by setting 
(x + -1.75) equal to 5.202163012 and -5.202163012.


Subproblem 1
x + -1.75 = 5.202163012

Simplifying
x + -1.75 = 5.202163012

Reorder the terms:
-1.75 + x = 5.202163012

Solving
-1.75 + x = 5.202163012

Solving for variable 'x'.

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

Add '1.75' to each side of the equation.
-1.75 + 1.75 + x = 5.202163012 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + x = 5.202163012 + 1.75
x = 5.202163012 + 1.75

Combine like terms: 5.202163012 + 1.75 = 6.952163012
x = 6.952163012

Simplifying
x = 6.952163012


Subproblem 2
x + -1.75 = -5.202163012

Simplifying
x + -1.75 = -5.202163012

Reorder the terms:
-1.75 + x = -5.202163012

Solving
-1.75 + x = -5.202163012

Solving for variable 'x'.

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

Add '1.75' to each side of the equation.
-1.75 + 1.75 + x = -5.202163012 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + x = -5.202163012 + 1.75
x = -5.202163012 + 1.75

Combine like terms: -5.202163012 + 1.75 = -3.452163012
x = -3.452163012

Simplifying
x = -3.452163012


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.952163012, -3.452163012}
Solution
x = {6.952163012, -3.452163012}

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