2x^2-10x-32=0

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Solution for 2x^2-10x-32=0 equation: 


Simplifying
2x2 + -10x + -32 = 0

Reorder the terms:
-32 + -10x + 2x2 = 0

Solving
-32 + -10x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-16 + -5x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-16 + -5x + x2)' equal to zero and attempt to solve:

Simplifying
-16 + -5x + x2 = 0

Solving
-16 + -5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + -5x + 16 + x2 = 0 + 16

Reorder the terms:
-16 + 16 + -5x + x2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -5x + x2 = 0 + 16
-5x + x2 = 0 + 16

Combine like terms: 0 + 16 = 16
-5x + x2 = 16

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 = 16 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 16 + 6.25

Combine like terms: 16 + 6.25 = 22.25
6.25 + -5x + x2 = 22.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 22.25

Calculate the square root of the right side: 4.716990566

Break this problem into two subproblems by setting 
(x + -2.5) equal to 4.716990566 and -4.716990566.


Subproblem 1
x + -2.5 = 4.716990566

Simplifying
x + -2.5 = 4.716990566

Reorder the terms:
-2.5 + x = 4.716990566

Solving
-2.5 + x = 4.716990566

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 = 4.716990566 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 4.716990566 + 2.5
x = 4.716990566 + 2.5

Combine like terms: 4.716990566 + 2.5 = 7.216990566
x = 7.216990566

Simplifying
x = 7.216990566


Subproblem 2
x + -2.5 = -4.716990566

Simplifying
x + -2.5 = -4.716990566

Reorder the terms:
-2.5 + x = -4.716990566

Solving
-2.5 + x = -4.716990566

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 = -4.716990566 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -4.716990566 + 2.5
x = -4.716990566 + 2.5

Combine like terms: -4.716990566 + 2.5 = -2.216990566
x = -2.216990566

Simplifying
x = -2.216990566


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.216990566, -2.216990566}
Solution
x = {7.216990566, -2.216990566}

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