8k^2-24k-144=8

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Solution for 8k^2-24k-144=8 equation: 


Simplifying
8k2 + -24k + -144 = 8

Reorder the terms:
-144 + -24k + 8k2 = 8

Solving
-144 + -24k + 8k2 = 8

Solving for variable 'k'.

Reorder the terms:
-144 + -8 + -24k + 8k2 = 8 + -8

Combine like terms: -144 + -8 = -152
-152 + -24k + 8k2 = 8 + -8

Combine like terms: 8 + -8 = 0
-152 + -24k + 8k2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-19 + -3k + k2) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(-19 + -3k + k2)' equal to zero and attempt to solve:

Simplifying
-19 + -3k + k2 = 0

Solving
-19 + -3k + k2 = 0

Begin completing the square.

Move the constant term to the right:

Add '19' to each side of the equation.
-19 + -3k + 19 + k2 = 0 + 19

Reorder the terms:
-19 + 19 + -3k + k2 = 0 + 19

Combine like terms: -19 + 19 = 0
0 + -3k + k2 = 0 + 19
-3k + k2 = 0 + 19

Combine like terms: 0 + 19 = 19
-3k + k2 = 19

The k term is -3k.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3k + 2.25 + k2 = 19 + 2.25

Reorder the terms:
2.25 + -3k + k2 = 19 + 2.25

Combine like terms: 19 + 2.25 = 21.25
2.25 + -3k + k2 = 21.25

Factor a perfect square on the left side:
(k + -1.5)(k + -1.5) = 21.25

Calculate the square root of the right side: 4.609772229

Break this problem into two subproblems by setting 
(k + -1.5) equal to 4.609772229 and -4.609772229.


Subproblem 1
k + -1.5 = 4.609772229

Simplifying
k + -1.5 = 4.609772229

Reorder the terms:
-1.5 + k = 4.609772229

Solving
-1.5 + k = 4.609772229

Solving for variable 'k'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + k = 4.609772229 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + k = 4.609772229 + 1.5
k = 4.609772229 + 1.5

Combine like terms: 4.609772229 + 1.5 = 6.109772229
k = 6.109772229

Simplifying
k = 6.109772229


Subproblem 2
k + -1.5 = -4.609772229

Simplifying
k + -1.5 = -4.609772229

Reorder the terms:
-1.5 + k = -4.609772229

Solving
-1.5 + k = -4.609772229

Solving for variable 'k'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + k = -4.609772229 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + k = -4.609772229 + 1.5
k = -4.609772229 + 1.5

Combine like terms: -4.609772229 + 1.5 = -3.109772229
k = -3.109772229

Simplifying
k = -3.109772229


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {6.109772229, -3.109772229}
Solution
k = {6.109772229, -3.109772229}

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