2x^2+36x-32=0

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Solution for 2x^2+36x-32=0 equation: 


Simplifying
2x2 + 36x + -32 = 0

Reorder the terms:
-32 + 36x + 2x2 = 0

Solving
-32 + 36x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-16 + 18x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-16 + 18x + x2)' equal to zero and attempt to solve:

Simplifying
-16 + 18x + x2 = 0

Solving
-16 + 18x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + 18x + 16 + x2 = 0 + 16

Reorder the terms:
-16 + 16 + 18x + x2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 18x + x2 = 0 + 16
18x + x2 = 0 + 16

Combine like terms: 0 + 16 = 16
18x + x2 = 16

The x term is 18x.  Take half its coefficient (9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
18x + 81 + x2 = 16 + 81

Reorder the terms:
81 + 18x + x2 = 16 + 81

Combine like terms: 16 + 81 = 97
81 + 18x + x2 = 97

Factor a perfect square on the left side:
(x + 9)(x + 9) = 97

Calculate the square root of the right side: 9.848857802

Break this problem into two subproblems by setting 
(x + 9) equal to 9.848857802 and -9.848857802.


Subproblem 1
x + 9 = 9.848857802

Simplifying
x + 9 = 9.848857802

Reorder the terms:
9 + x = 9.848857802

Solving
9 + x = 9.848857802

Solving for variable 'x'.

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

Add '-9' to each side of the equation.
9 + -9 + x = 9.848857802 + -9

Combine like terms: 9 + -9 = 0
0 + x = 9.848857802 + -9
x = 9.848857802 + -9

Combine like terms: 9.848857802 + -9 = 0.848857802
x = 0.848857802

Simplifying
x = 0.848857802


Subproblem 2
x + 9 = -9.848857802

Simplifying
x + 9 = -9.848857802

Reorder the terms:
9 + x = -9.848857802

Solving
9 + x = -9.848857802

Solving for variable 'x'.

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

Add '-9' to each side of the equation.
9 + -9 + x = -9.848857802 + -9

Combine like terms: 9 + -9 = 0
0 + x = -9.848857802 + -9
x = -9.848857802 + -9

Combine like terms: -9.848857802 + -9 = -18.848857802
x = -18.848857802

Simplifying
x = -18.848857802


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.848857802, -18.848857802}
Solution
x = {0.848857802, -18.848857802}

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