4x^2+10x-96=0

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Solution for 4x^2+10x-96=0 equation: 


Simplifying
4x2 + 10x + -96 = 0

Reorder the terms:
-96 + 10x + 4x2 = 0

Solving
-96 + 10x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-48 + 5x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-48 + 5x + 2x2)' equal to zero and attempt to solve:

Simplifying
-48 + 5x + 2x2 = 0

Solving
-48 + 5x + 2x2 = 0

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

Divide each side by '2'.
-24 + 2.5x + x2 = 0

Move the constant term to the right:

Add '24' to each side of the equation.
-24 + 2.5x + 24 + x2 = 0 + 24

Reorder the terms:
-24 + 24 + 2.5x + x2 = 0 + 24

Combine like terms: -24 + 24 = 0
0 + 2.5x + x2 = 0 + 24
2.5x + x2 = 0 + 24

Combine like terms: 0 + 24 = 24
2.5x + x2 = 24

The x term is 2.5x.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x + 1.5625 + x2 = 24 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = 24 + 1.5625

Combine like terms: 24 + 1.5625 = 25.5625
1.5625 + 2.5x + x2 = 25.5625

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 25.5625

Calculate the square root of the right side: 5.055937104

Break this problem into two subproblems by setting 
(x + 1.25) equal to 5.055937104 and -5.055937104.


Subproblem 1
x + 1.25 = 5.055937104

Simplifying
x + 1.25 = 5.055937104

Reorder the terms:
1.25 + x = 5.055937104

Solving
1.25 + x = 5.055937104

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = 5.055937104 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = 5.055937104 + -1.25
x = 5.055937104 + -1.25

Combine like terms: 5.055937104 + -1.25 = 3.805937104
x = 3.805937104

Simplifying
x = 3.805937104


Subproblem 2
x + 1.25 = -5.055937104

Simplifying
x + 1.25 = -5.055937104

Reorder the terms:
1.25 + x = -5.055937104

Solving
1.25 + x = -5.055937104

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = -5.055937104 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = -5.055937104 + -1.25
x = -5.055937104 + -1.25

Combine like terms: -5.055937104 + -1.25 = -6.305937104
x = -6.305937104

Simplifying
x = -6.305937104


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.805937104, -6.305937104}
Solution
x = {3.805937104, -6.305937104}

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