2x^2+16x-48=0

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Solution for 2x^2+16x-48=0 equation: 


Simplifying
2x2 + 16x + -48 = 0

Reorder the terms:
-48 + 16x + 2x2 = 0

Solving
-48 + 16x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-24 + 8x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-24 + 8x + x2)' equal to zero and attempt to solve:

Simplifying
-24 + 8x + x2 = 0

Solving
-24 + 8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '24' to each side of the equation.
-24 + 8x + 24 + x2 = 0 + 24

Reorder the terms:
-24 + 24 + 8x + x2 = 0 + 24

Combine like terms: -24 + 24 = 0
0 + 8x + x2 = 0 + 24
8x + x2 = 0 + 24

Combine like terms: 0 + 24 = 24
8x + x2 = 24

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = 24 + 16

Reorder the terms:
16 + 8x + x2 = 24 + 16

Combine like terms: 24 + 16 = 40
16 + 8x + x2 = 40

Factor a perfect square on the left side:
(x + 4)(x + 4) = 40

Calculate the square root of the right side: 6.32455532

Break this problem into two subproblems by setting 
(x + 4) equal to 6.32455532 and -6.32455532.


Subproblem 1
x + 4 = 6.32455532

Simplifying
x + 4 = 6.32455532

Reorder the terms:
4 + x = 6.32455532

Solving
4 + x = 6.32455532

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = 6.32455532 + -4

Combine like terms: 4 + -4 = 0
0 + x = 6.32455532 + -4
x = 6.32455532 + -4

Combine like terms: 6.32455532 + -4 = 2.32455532
x = 2.32455532

Simplifying
x = 2.32455532


Subproblem 2
x + 4 = -6.32455532

Simplifying
x + 4 = -6.32455532

Reorder the terms:
4 + x = -6.32455532

Solving
4 + x = -6.32455532

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = -6.32455532 + -4

Combine like terms: 4 + -4 = 0
0 + x = -6.32455532 + -4
x = -6.32455532 + -4

Combine like terms: -6.32455532 + -4 = -10.32455532
x = -10.32455532

Simplifying
x = -10.32455532


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.32455532, -10.32455532}
Solution
x = {2.32455532, -10.32455532}

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