-8k(k+6)=-5k+2(k-4)

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Solution for -8k(k+6)=-5k+2(k-4) equation:


Simplifying
-8k(k + 6) = -5k + 2(k + -4)

Reorder the terms:
-8k(6 + k) = -5k + 2(k + -4)
(6 * -8k + k * -8k) = -5k + 2(k + -4)
(-48k + -8k2) = -5k + 2(k + -4)

Reorder the terms:
-48k + -8k2 = -5k + 2(-4 + k)
-48k + -8k2 = -5k + (-4 * 2 + k * 2)
-48k + -8k2 = -5k + (-8 + 2k)

Reorder the terms:
-48k + -8k2 = -8 + -5k + 2k

Combine like terms: -5k + 2k = -3k
-48k + -8k2 = -8 + -3k

Solving
-48k + -8k2 = -8 + -3k

Solving for variable 'k'.

Reorder the terms:
8 + -48k + 3k + -8k2 = -8 + -3k + 8 + 3k

Combine like terms: -48k + 3k = -45k
8 + -45k + -8k2 = -8 + -3k + 8 + 3k

Reorder the terms:
8 + -45k + -8k2 = -8 + 8 + -3k + 3k

Combine like terms: -8 + 8 = 0
8 + -45k + -8k2 = 0 + -3k + 3k
8 + -45k + -8k2 = -3k + 3k

Combine like terms: -3k + 3k = 0
8 + -45k + -8k2 = 0

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
-1 + 5.625k + k2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 5.625k + 1 + k2 = 0 + 1

Reorder the terms:
-1 + 1 + 5.625k + k2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 5.625k + k2 = 0 + 1
5.625k + k2 = 0 + 1

Combine like terms: 0 + 1 = 1
5.625k + k2 = 1

The k term is 5.625k.  Take half its coefficient (2.8125).
Square it (7.91015625) and add it to both sides.

Add '7.91015625' to each side of the equation.
5.625k + 7.91015625 + k2 = 1 + 7.91015625

Reorder the terms:
7.91015625 + 5.625k + k2 = 1 + 7.91015625

Combine like terms: 1 + 7.91015625 = 8.91015625
7.91015625 + 5.625k + k2 = 8.91015625

Factor a perfect square on the left side:
(k + 2.8125)(k + 2.8125) = 8.91015625

Calculate the square root of the right side: 2.984988484

Break this problem into two subproblems by setting 
(k + 2.8125) equal to 2.984988484 and -2.984988484.

Subproblem 1

k + 2.8125 = 2.984988484 Simplifying k + 2.8125 = 2.984988484 Reorder the terms: 2.8125 + k = 2.984988484 Solving 2.8125 + k = 2.984988484 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-2.8125' to each side of the equation. 2.8125 + -2.8125 + k = 2.984988484 + -2.8125 Combine like terms: 2.8125 + -2.8125 = 0.0000 0.0000 + k = 2.984988484 + -2.8125 k = 2.984988484 + -2.8125 Combine like terms: 2.984988484 + -2.8125 = 0.172488484 k = 0.172488484 Simplifying k = 0.172488484

Subproblem 2

k + 2.8125 = -2.984988484 Simplifying k + 2.8125 = -2.984988484 Reorder the terms: 2.8125 + k = -2.984988484 Solving 2.8125 + k = -2.984988484 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-2.8125' to each side of the equation. 2.8125 + -2.8125 + k = -2.984988484 + -2.8125 Combine like terms: 2.8125 + -2.8125 = 0.0000 0.0000 + k = -2.984988484 + -2.8125 k = -2.984988484 + -2.8125 Combine like terms: -2.984988484 + -2.8125 = -5.797488484 k = -5.797488484 Simplifying k = -5.797488484

Solution

The solution to the problem is based on the solutions from the subproblems. k = {0.172488484, -5.797488484}

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