2x^2+16x=-12

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Solution for 2x^2+16x=-12 equation: 


Simplifying
2x2 + 16x = -12

Reorder the terms:
16x + 2x2 = -12

Solving
16x + 2x2 = -12

Solving for variable 'x'.

Reorder the terms:
12 + 16x + 2x2 = -12 + 12

Combine like terms: -12 + 12 = 0
12 + 16x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + 8x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(6 + 8x + x2)' equal to zero and attempt to solve:

Simplifying
6 + 8x + x2 = 0

Solving
6 + 8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + 8x + -6 + x2 = 0 + -6

Reorder the terms:
6 + -6 + 8x + x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 8x + x2 = 0 + -6
8x + x2 = 0 + -6

Combine like terms: 0 + -6 = -6
8x + x2 = -6

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 = -6 + 16

Reorder the terms:
16 + 8x + x2 = -6 + 16

Combine like terms: -6 + 16 = 10
16 + 8x + x2 = 10

Factor a perfect square on the left side:
(x + 4)(x + 4) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(x + 4) equal to 3.16227766 and -3.16227766.


Subproblem 1
x + 4 = 3.16227766

Simplifying
x + 4 = 3.16227766

Reorder the terms:
4 + x = 3.16227766

Solving
4 + x = 3.16227766

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 = 3.16227766 + -4

Combine like terms: 4 + -4 = 0
0 + x = 3.16227766 + -4
x = 3.16227766 + -4

Combine like terms: 3.16227766 + -4 = -0.83772234
x = -0.83772234

Simplifying
x = -0.83772234


Subproblem 2
x + 4 = -3.16227766

Simplifying
x + 4 = -3.16227766

Reorder the terms:
4 + x = -3.16227766

Solving
4 + x = -3.16227766

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 = -3.16227766 + -4

Combine like terms: 4 + -4 = 0
0 + x = -3.16227766 + -4
x = -3.16227766 + -4

Combine like terms: -3.16227766 + -4 = -7.16227766
x = -7.16227766

Simplifying
x = -7.16227766


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.83772234, -7.16227766}
Solution
x = {-0.83772234, -7.16227766}

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