x+x^2+4x-96=0

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


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

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

Combine like terms: x + 4x = 5x
-96 + 5x + x2 = 0

Solving
-96 + 5x + 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 + 5x + 96 + x2 = 0 + 96

Reorder the terms:
-96 + 96 + 5x + x2 = 0 + 96

Combine like terms: -96 + 96 = 0
0 + 5x + x2 = 0 + 96
5x + x2 = 0 + 96

Combine like terms: 0 + 96 = 96
5x + x2 = 96

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 96 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 96 + 6.25

Combine like terms: 96 + 6.25 = 102.25
6.25 + 5x + x2 = 102.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 102.25

Calculate the square root of the right side: 10.111874208

Break this problem into two subproblems by setting 
(x + 2.5) equal to 10.111874208 and -10.111874208.


Subproblem 1
x + 2.5 = 10.111874208

Simplifying
x + 2.5 = 10.111874208

Reorder the terms:
2.5 + x = 10.111874208

Solving
2.5 + x = 10.111874208

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 10.111874208 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 10.111874208 + -2.5
x = 10.111874208 + -2.5

Combine like terms: 10.111874208 + -2.5 = 7.611874208
x = 7.611874208

Simplifying
x = 7.611874208


Subproblem 2
x + 2.5 = -10.111874208

Simplifying
x + 2.5 = -10.111874208

Reorder the terms:
2.5 + x = -10.111874208

Solving
2.5 + x = -10.111874208

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -10.111874208 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -10.111874208 + -2.5
x = -10.111874208 + -2.5

Combine like terms: -10.111874208 + -2.5 = -12.611874208
x = -12.611874208

Simplifying
x = -12.611874208


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.611874208, -12.611874208}

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