k^2-3k-8=0

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Solution for k^2-3k-8=0 equation: 


Simplifying
k2 + -3k + -8 = 0

Reorder the terms:
-8 + -3k + k2 = 0

Solving
-8 + -3k + k2 = 0

Solving for variable 'k'.

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + -3k + 8 + k2 = 0 + 8

Reorder the terms:
-8 + 8 + -3k + k2 = 0 + 8

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

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

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 = 8 + 2.25

Reorder the terms:
2.25 + -3k + k2 = 8 + 2.25

Combine like terms: 8 + 2.25 = 10.25
2.25 + -3k + k2 = 10.25

Factor a perfect square on the left side:
(k + -1.5)(k + -1.5) = 10.25

Calculate the square root of the right side: 3.201562119

Break this problem into two subproblems by setting 
(k + -1.5) equal to 3.201562119 and -3.201562119.


Subproblem 1
k + -1.5 = 3.201562119

Simplifying
k + -1.5 = 3.201562119

Reorder the terms:
-1.5 + k = 3.201562119

Solving
-1.5 + k = 3.201562119

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 = 3.201562119 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + k = 3.201562119 + 1.5
k = 3.201562119 + 1.5

Combine like terms: 3.201562119 + 1.5 = 4.701562119
k = 4.701562119

Simplifying
k = 4.701562119


Subproblem 2
k + -1.5 = -3.201562119

Simplifying
k + -1.5 = -3.201562119

Reorder the terms:
-1.5 + k = -3.201562119

Solving
-1.5 + k = -3.201562119

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 = -3.201562119 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + k = -3.201562119 + 1.5
k = -3.201562119 + 1.5

Combine like terms: -3.201562119 + 1.5 = -1.701562119
k = -1.701562119

Simplifying
k = -1.701562119


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {4.701562119, -1.701562119}

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