2x^2+10x-88=0

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Solution for 2x^2+10x-88=0 equation: 


Simplifying
2x2 + 10x + -88 = 0

Reorder the terms:
-88 + 10x + 2x2 = 0

Solving
-88 + 10x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-44 + 5x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-44 + 5x + x2)' equal to zero and attempt to solve:

Simplifying
-44 + 5x + x2 = 0

Solving
-44 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '44' to each side of the equation.
-44 + 5x + 44 + x2 = 0 + 44

Reorder the terms:
-44 + 44 + 5x + x2 = 0 + 44

Combine like terms: -44 + 44 = 0
0 + 5x + x2 = 0 + 44
5x + x2 = 0 + 44

Combine like terms: 0 + 44 = 44
5x + x2 = 44

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 = 44 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 44 + 6.25

Combine like terms: 44 + 6.25 = 50.25
6.25 + 5x + x2 = 50.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 50.25

Calculate the square root of the right side: 7.088723439

Break this problem into two subproblems by setting 
(x + 2.5) equal to 7.088723439 and -7.088723439.


Subproblem 1
x + 2.5 = 7.088723439

Simplifying
x + 2.5 = 7.088723439

Reorder the terms:
2.5 + x = 7.088723439

Solving
2.5 + x = 7.088723439

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 = 7.088723439 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 7.088723439 + -2.5
x = 7.088723439 + -2.5

Combine like terms: 7.088723439 + -2.5 = 4.588723439
x = 4.588723439

Simplifying
x = 4.588723439


Subproblem 2
x + 2.5 = -7.088723439

Simplifying
x + 2.5 = -7.088723439

Reorder the terms:
2.5 + x = -7.088723439

Solving
2.5 + x = -7.088723439

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 = -7.088723439 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -7.088723439 + -2.5
x = -7.088723439 + -2.5

Combine like terms: -7.088723439 + -2.5 = -9.588723439
x = -9.588723439

Simplifying
x = -9.588723439


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.588723439, -9.588723439}
Solution
x = {4.588723439, -9.588723439}

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