2x^2+32x-48=0

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Solution for 2x^2+32x-48=0 equation: 


Simplifying
2x2 + 32x + -48 = 0

Reorder the terms:
-48 + 32x + 2x2 = 0

Solving
-48 + 32x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-24 + 16x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-24 + 16x + x2)' equal to zero and attempt to solve:

Simplifying
-24 + 16x + x2 = 0

Solving
-24 + 16x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '24' to each side of the equation.
-24 + 16x + 24 + x2 = 0 + 24

Reorder the terms:
-24 + 24 + 16x + x2 = 0 + 24

Combine like terms: -24 + 24 = 0
0 + 16x + x2 = 0 + 24
16x + x2 = 0 + 24

Combine like terms: 0 + 24 = 24
16x + x2 = 24

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 = 24 + 64

Reorder the terms:
64 + 16x + x2 = 24 + 64

Combine like terms: 24 + 64 = 88
64 + 16x + x2 = 88

Factor a perfect square on the left side:
(x + 8)(x + 8) = 88

Calculate the square root of the right side: 9.38083152

Break this problem into two subproblems by setting 
(x + 8) equal to 9.38083152 and -9.38083152.


Subproblem 1
x + 8 = 9.38083152

Simplifying
x + 8 = 9.38083152

Reorder the terms:
8 + x = 9.38083152

Solving
8 + x = 9.38083152

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 = 9.38083152 + -8

Combine like terms: 8 + -8 = 0
0 + x = 9.38083152 + -8
x = 9.38083152 + -8

Combine like terms: 9.38083152 + -8 = 1.38083152
x = 1.38083152

Simplifying
x = 1.38083152


Subproblem 2
x + 8 = -9.38083152

Simplifying
x + 8 = -9.38083152

Reorder the terms:
8 + x = -9.38083152

Solving
8 + x = -9.38083152

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 = -9.38083152 + -8

Combine like terms: 8 + -8 = 0
0 + x = -9.38083152 + -8
x = -9.38083152 + -8

Combine like terms: -9.38083152 + -8 = -17.38083152
x = -17.38083152

Simplifying
x = -17.38083152


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.38083152, -17.38083152}
Solution
x = {1.38083152, -17.38083152}

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