2x^2-32x-56=0

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Solution for 2x^2-32x-56=0 equation: 


Simplifying
2x2 + -32x + -56 = 0

Reorder the terms:
-56 + -32x + 2x2 = 0

Solving
-56 + -32x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-28 + -16x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-28 + -16x + x2)' equal to zero and attempt to solve:

Simplifying
-28 + -16x + x2 = 0

Solving
-28 + -16x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '28' to each side of the equation.
-28 + -16x + 28 + x2 = 0 + 28

Reorder the terms:
-28 + 28 + -16x + x2 = 0 + 28

Combine like terms: -28 + 28 = 0
0 + -16x + x2 = 0 + 28
-16x + x2 = 0 + 28

Combine like terms: 0 + 28 = 28
-16x + x2 = 28

The x term is -16x.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16x + 64 + x2 = 28 + 64

Reorder the terms:
64 + -16x + x2 = 28 + 64

Combine like terms: 28 + 64 = 92
64 + -16x + x2 = 92

Factor a perfect square on the left side:
(x + -8)(x + -8) = 92

Calculate the square root of the right side: 9.591663047

Break this problem into two subproblems by setting 
(x + -8) equal to 9.591663047 and -9.591663047.


Subproblem 1
x + -8 = 9.591663047

Simplifying
x + -8 = 9.591663047

Reorder the terms:
-8 + x = 9.591663047

Solving
-8 + x = 9.591663047

Solving for variable 'x'.

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

Add '8' to each side of the equation.
-8 + 8 + x = 9.591663047 + 8

Combine like terms: -8 + 8 = 0
0 + x = 9.591663047 + 8
x = 9.591663047 + 8

Combine like terms: 9.591663047 + 8 = 17.591663047
x = 17.591663047

Simplifying
x = 17.591663047


Subproblem 2
x + -8 = -9.591663047

Simplifying
x + -8 = -9.591663047

Reorder the terms:
-8 + x = -9.591663047

Solving
-8 + x = -9.591663047

Solving for variable 'x'.

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

Add '8' to each side of the equation.
-8 + 8 + x = -9.591663047 + 8

Combine like terms: -8 + 8 = 0
0 + x = -9.591663047 + 8
x = -9.591663047 + 8

Combine like terms: -9.591663047 + 8 = -1.591663047
x = -1.591663047

Simplifying
x = -1.591663047


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17.591663047, -1.591663047}
Solution
x = {17.591663047, -1.591663047}

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