2x^2+16x-24=0

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Solution for 2x^2+16x-24=0 equation: 


Simplifying
2x2 + 16x + -24 = 0

Reorder the terms:
-24 + 16x + 2x2 = 0

Solving
-24 + 16x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + 8x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-12 + 8x + x2)' equal to zero and attempt to solve:

Simplifying
-12 + 8x + x2 = 0

Solving
-12 + 8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + 8x + 12 + x2 = 0 + 12

Reorder the terms:
-12 + 12 + 8x + x2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + 8x + x2 = 0 + 12
8x + x2 = 0 + 12

Combine like terms: 0 + 12 = 12
8x + x2 = 12

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 = 12 + 16

Reorder the terms:
16 + 8x + x2 = 12 + 16

Combine like terms: 12 + 16 = 28
16 + 8x + x2 = 28

Factor a perfect square on the left side:
(x + 4)(x + 4) = 28

Calculate the square root of the right side: 5.291502622

Break this problem into two subproblems by setting 
(x + 4) equal to 5.291502622 and -5.291502622.


Subproblem 1
x + 4 = 5.291502622

Simplifying
x + 4 = 5.291502622

Reorder the terms:
4 + x = 5.291502622

Solving
4 + x = 5.291502622

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 = 5.291502622 + -4

Combine like terms: 4 + -4 = 0
0 + x = 5.291502622 + -4
x = 5.291502622 + -4

Combine like terms: 5.291502622 + -4 = 1.291502622
x = 1.291502622

Simplifying
x = 1.291502622


Subproblem 2
x + 4 = -5.291502622

Simplifying
x + 4 = -5.291502622

Reorder the terms:
4 + x = -5.291502622

Solving
4 + x = -5.291502622

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 = -5.291502622 + -4

Combine like terms: 4 + -4 = 0
0 + x = -5.291502622 + -4
x = -5.291502622 + -4

Combine like terms: -5.291502622 + -4 = -9.291502622
x = -9.291502622

Simplifying
x = -9.291502622


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.291502622, -9.291502622}
Solution
x = {1.291502622, -9.291502622}

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