2x^2-14x-32=0

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Solution for 2x^2-14x-32=0 equation: 


Simplifying
2x2 + -14x + -32 = 0

Reorder the terms:
-32 + -14x + 2x2 = 0

Solving
-32 + -14x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-16 + -7x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-16 + -7x + x2)' equal to zero and attempt to solve:

Simplifying
-16 + -7x + x2 = 0

Solving
-16 + -7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + -7x + 16 + x2 = 0 + 16

Reorder the terms:
-16 + 16 + -7x + x2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -7x + x2 = 0 + 16
-7x + x2 = 0 + 16

Combine like terms: 0 + 16 = 16
-7x + x2 = 16

The x term is -7x.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7x + 12.25 + x2 = 16 + 12.25

Reorder the terms:
12.25 + -7x + x2 = 16 + 12.25

Combine like terms: 16 + 12.25 = 28.25
12.25 + -7x + x2 = 28.25

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 28.25

Calculate the square root of the right side: 5.315072906

Break this problem into two subproblems by setting 
(x + -3.5) equal to 5.315072906 and -5.315072906.


Subproblem 1
x + -3.5 = 5.315072906

Simplifying
x + -3.5 = 5.315072906

Reorder the terms:
-3.5 + x = 5.315072906

Solving
-3.5 + x = 5.315072906

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = 5.315072906 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = 5.315072906 + 3.5
x = 5.315072906 + 3.5

Combine like terms: 5.315072906 + 3.5 = 8.815072906
x = 8.815072906

Simplifying
x = 8.815072906


Subproblem 2
x + -3.5 = -5.315072906

Simplifying
x + -3.5 = -5.315072906

Reorder the terms:
-3.5 + x = -5.315072906

Solving
-3.5 + x = -5.315072906

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = -5.315072906 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = -5.315072906 + 3.5
x = -5.315072906 + 3.5

Combine like terms: -5.315072906 + 3.5 = -1.815072906
x = -1.815072906

Simplifying
x = -1.815072906


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.815072906, -1.815072906}
Solution
x = {8.815072906, -1.815072906}

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