2k^2+16k=-12

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


Simplifying
2k2 + 16k = -12

Reorder the terms:
16k + 2k2 = -12

Solving
16k + 2k2 = -12

Solving for variable 'k'.

Reorder the terms:
12 + 16k + 2k2 = -12 + 12

Combine like terms: -12 + 12 = 0
12 + 16k + 2k2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + 8k + k2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(6 + 8k + k2)' equal to zero and attempt to solve:

Simplifying
6 + 8k + k2 = 0

Solving
6 + 8k + k2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + 8k + -6 + k2 = 0 + -6

Reorder the terms:
6 + -6 + 8k + k2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 8k + k2 = 0 + -6
8k + k2 = 0 + -6

Combine like terms: 0 + -6 = -6
8k + k2 = -6

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

Add '16' to each side of the equation.
8k + 16 + k2 = -6 + 16

Reorder the terms:
16 + 8k + k2 = -6 + 16

Combine like terms: -6 + 16 = 10
16 + 8k + k2 = 10

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

Calculate the square root of the right side: 3.16227766

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


Subproblem 1
k + 4 = 3.16227766

Simplifying
k + 4 = 3.16227766

Reorder the terms:
4 + k = 3.16227766

Solving
4 + k = 3.16227766

Solving for variable 'k'.

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

Add '-4' to each side of the equation.
4 + -4 + k = 3.16227766 + -4

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

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

Simplifying
k = -0.83772234


Subproblem 2
k + 4 = -3.16227766

Simplifying
k + 4 = -3.16227766

Reorder the terms:
4 + k = -3.16227766

Solving
4 + k = -3.16227766

Solving for variable 'k'.

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

Add '-4' to each side of the equation.
4 + -4 + k = -3.16227766 + -4

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

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

Simplifying
k = -7.16227766


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

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