2x^2+40x+32=0

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Solution for 2x^2+40x+32=0 equation: 


Simplifying
2x2 + 40x + 32 = 0

Reorder the terms:
32 + 40x + 2x2 = 0

Solving
32 + 40x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(16 + 20x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(16 + 20x + x2)' equal to zero and attempt to solve:

Simplifying
16 + 20x + x2 = 0

Solving
16 + 20x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-16' to each side of the equation.
16 + 20x + -16 + x2 = 0 + -16

Reorder the terms:
16 + -16 + 20x + x2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + 20x + x2 = 0 + -16
20x + x2 = 0 + -16

Combine like terms: 0 + -16 = -16
20x + x2 = -16

The x term is 20x.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20x + 100 + x2 = -16 + 100

Reorder the terms:
100 + 20x + x2 = -16 + 100

Combine like terms: -16 + 100 = 84
100 + 20x + x2 = 84

Factor a perfect square on the left side:
(x + 10)(x + 10) = 84

Calculate the square root of the right side: 9.16515139

Break this problem into two subproblems by setting 
(x + 10) equal to 9.16515139 and -9.16515139.


Subproblem 1
x + 10 = 9.16515139

Simplifying
x + 10 = 9.16515139

Reorder the terms:
10 + x = 9.16515139

Solving
10 + x = 9.16515139

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = 9.16515139 + -10

Combine like terms: 10 + -10 = 0
0 + x = 9.16515139 + -10
x = 9.16515139 + -10

Combine like terms: 9.16515139 + -10 = -0.83484861
x = -0.83484861

Simplifying
x = -0.83484861


Subproblem 2
x + 10 = -9.16515139

Simplifying
x + 10 = -9.16515139

Reorder the terms:
10 + x = -9.16515139

Solving
10 + x = -9.16515139

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = -9.16515139 + -10

Combine like terms: 10 + -10 = 0
0 + x = -9.16515139 + -10
x = -9.16515139 + -10

Combine like terms: -9.16515139 + -10 = -19.16515139
x = -19.16515139

Simplifying
x = -19.16515139


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.83484861, -19.16515139}
Solution
x = {-0.83484861, -19.16515139}

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