20k^2-52k=25

Solution for 20k^2-52k=25 equation:

Simplifying
20k2 + -52k = 25

Reorder the terms:
-52k + 20k2 = 25

Solving
-52k + 20k2 = 25

Solving for variable 'k'.

Reorder the terms:
-25 + -52k + 20k2 = 25 + -25

Combine like terms: 25 + -25 = 0
-25 + -52k + 20k2 = 0

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

Divide each side by '20'.
-1.25 + -2.6k + k2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + -2.6k + 1.25 + k2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + -2.6k + k2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + -2.6k + k2 = 0 + 1.25
-2.6k + k2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
-2.6k + k2 = 1.25

The k term is -2.6k.  Take half its coefficient (-1.3).
Square it (1.69) and add it to both sides.

Add '1.69' to each side of the equation.
-2.6k + 1.69 + k2 = 1.25 + 1.69

Reorder the terms:
1.69 + -2.6k + k2 = 1.25 + 1.69

Combine like terms: 1.25 + 1.69 = 2.94
1.69 + -2.6k + k2 = 2.94

Factor a perfect square on the left side:
(k + -1.3)(k + -1.3) = 2.94

Calculate the square root of the right side: 1.71464282

Break this problem into two subproblems by setting 
(k + -1.3) equal to 1.71464282 and -1.71464282.

Subproblem 1
k + -1.3 = 1.71464282

Simplifying
k + -1.3 = 1.71464282

Reorder the terms:
-1.3 + k = 1.71464282

Solving
-1.3 + k = 1.71464282

Solving for variable 'k'.

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

Add '1.3' to each side of the equation.
-1.3 + 1.3 + k = 1.71464282 + 1.3

Combine like terms: -1.3 + 1.3 = 0.0
0.0 + k = 1.71464282 + 1.3
k = 1.71464282 + 1.3

Combine like terms: 1.71464282 + 1.3 = 3.01464282
k = 3.01464282

Simplifying
k = 3.01464282

Subproblem 2
k + -1.3 = -1.71464282

Simplifying
k + -1.3 = -1.71464282

Reorder the terms:
-1.3 + k = -1.71464282

Solving
-1.3 + k = -1.71464282

Solving for variable 'k'.

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

Add '1.3' to each side of the equation.
-1.3 + 1.3 + k = -1.71464282 + 1.3

Combine like terms: -1.3 + 1.3 = 0.0
0.0 + k = -1.71464282 + 1.3
k = -1.71464282 + 1.3

Combine like terms: -1.71464282 + 1.3 = -0.41464282
k = -0.41464282

Simplifying
k = -0.41464282

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {3.01464282, -0.41464282}