x^2-3x-96=0

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Solution for x^2-3x-96=0 equation: 


Simplifying
x2 + -3x + -96 = 0

Reorder the terms:
-96 + -3x + x2 = 0

Solving
-96 + -3x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '96' to each side of the equation.
-96 + -3x + 96 + x2 = 0 + 96

Reorder the terms:
-96 + 96 + -3x + x2 = 0 + 96

Combine like terms: -96 + 96 = 0
0 + -3x + x2 = 0 + 96
-3x + x2 = 0 + 96

Combine like terms: 0 + 96 = 96
-3x + x2 = 96

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 96 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 96 + 2.25

Combine like terms: 96 + 2.25 = 98.25
2.25 + -3x + x2 = 98.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 98.25

Calculate the square root of the right side: 9.912113801

Break this problem into two subproblems by setting 
(x + -1.5) equal to 9.912113801 and -9.912113801.


Subproblem 1
x + -1.5 = 9.912113801

Simplifying
x + -1.5 = 9.912113801

Reorder the terms:
-1.5 + x = 9.912113801

Solving
-1.5 + x = 9.912113801

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = 9.912113801 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 9.912113801 + 1.5
x = 9.912113801 + 1.5

Combine like terms: 9.912113801 + 1.5 = 11.412113801
x = 11.412113801

Simplifying
x = 11.412113801


Subproblem 2
x + -1.5 = -9.912113801

Simplifying
x + -1.5 = -9.912113801

Reorder the terms:
-1.5 + x = -9.912113801

Solving
-1.5 + x = -9.912113801

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = -9.912113801 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -9.912113801 + 1.5
x = -9.912113801 + 1.5

Combine like terms: -9.912113801 + 1.5 = -8.412113801
x = -8.412113801

Simplifying
x = -8.412113801


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.412113801, -8.412113801}

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