2k^2-30k-100=0

Solution for 2k^2-30k-100=0 equation:

Simplifying
2k2 + -30k + -100 = 0

Reorder the terms:
-100 + -30k + 2k2 = 0

Solving
-100 + -30k + 2k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-50 + -15k + k2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-50 + -15k + k2)' equal to zero and attempt to solve:

Simplifying
-50 + -15k + k2 = 0

Solving
-50 + -15k + k2 = 0

Begin completing the square.

Move the constant term to the right:

Add '50' to each side of the equation.
-50 + -15k + 50 + k2 = 0 + 50

Reorder the terms:
-50 + 50 + -15k + k2 = 0 + 50

Combine like terms: -50 + 50 = 0
0 + -15k + k2 = 0 + 50
-15k + k2 = 0 + 50

Combine like terms: 0 + 50 = 50
-15k + k2 = 50

The k term is -15k.  Take half its coefficient (-7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
-15k + 56.25 + k2 = 50 + 56.25

Reorder the terms:
56.25 + -15k + k2 = 50 + 56.25

Combine like terms: 50 + 56.25 = 106.25
56.25 + -15k + k2 = 106.25

Factor a perfect square on the left side:
(k + -7.5)(k + -7.5) = 106.25

Calculate the square root of the right side: 10.307764064

Break this problem into two subproblems by setting 
(k + -7.5) equal to 10.307764064 and -10.307764064.

Subproblem 1
k + -7.5 = 10.307764064

Simplifying
k + -7.5 = 10.307764064

Reorder the terms:
-7.5 + k = 10.307764064

Solving
-7.5 + k = 10.307764064

Solving for variable 'k'.

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

Add '7.5' to each side of the equation.
-7.5 + 7.5 + k = 10.307764064 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + k = 10.307764064 + 7.5
k = 10.307764064 + 7.5

Combine like terms: 10.307764064 + 7.5 = 17.807764064
k = 17.807764064

Simplifying
k = 17.807764064

Subproblem 2
k + -7.5 = -10.307764064

Simplifying
k + -7.5 = -10.307764064

Reorder the terms:
-7.5 + k = -10.307764064

Solving
-7.5 + k = -10.307764064

Solving for variable 'k'.

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

Add '7.5' to each side of the equation.
-7.5 + 7.5 + k = -10.307764064 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + k = -10.307764064 + 7.5
k = -10.307764064 + 7.5

Combine like terms: -10.307764064 + 7.5 = -2.807764064
k = -2.807764064

Simplifying
k = -2.807764064

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {17.807764064, -2.807764064}
Solution
k = {17.807764064, -2.807764064}