k^2-25k+16=0

Solution for k^2-25k+16=0 equation:

Simplifying
k2 + -25k + 16 = 0

Reorder the terms:
16 + -25k + k2 = 0

Solving
16 + -25k + k2 = 0

Solving for variable 'k'.

Begin completing the square.

Move the constant term to the right:

Add '-16' to each side of the equation.
16 + -25k + -16 + k2 = 0 + -16

Reorder the terms:
16 + -16 + -25k + k2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -25k + k2 = 0 + -16
-25k + k2 = 0 + -16

Combine like terms: 0 + -16 = -16
-25k + k2 = -16

The k term is -25k.  Take half its coefficient (-12.5).
Square it (156.25) and add it to both sides.

Add '156.25' to each side of the equation.
-25k + 156.25 + k2 = -16 + 156.25

Reorder the terms:
156.25 + -25k + k2 = -16 + 156.25

Combine like terms: -16 + 156.25 = 140.25
156.25 + -25k + k2 = 140.25

Factor a perfect square on the left side:
(k + -12.5)(k + -12.5) = 140.25

Calculate the square root of the right side: 11.842719282

Break this problem into two subproblems by setting 
(k + -12.5) equal to 11.842719282 and -11.842719282.

Subproblem 1
k + -12.5 = 11.842719282

Simplifying
k + -12.5 = 11.842719282

Reorder the terms:
-12.5 + k = 11.842719282

Solving
-12.5 + k = 11.842719282

Solving for variable 'k'.

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

Add '12.5' to each side of the equation.
-12.5 + 12.5 + k = 11.842719282 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + k = 11.842719282 + 12.5
k = 11.842719282 + 12.5

Combine like terms: 11.842719282 + 12.5 = 24.342719282
k = 24.342719282

Simplifying
k = 24.342719282

Subproblem 2
k + -12.5 = -11.842719282

Simplifying
k + -12.5 = -11.842719282

Reorder the terms:
-12.5 + k = -11.842719282

Solving
-12.5 + k = -11.842719282

Solving for variable 'k'.

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

Add '12.5' to each side of the equation.
-12.5 + 12.5 + k = -11.842719282 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + k = -11.842719282 + 12.5
k = -11.842719282 + 12.5

Combine like terms: -11.842719282 + 12.5 = 0.657280718
k = 0.657280718

Simplifying
k = 0.657280718

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {24.342719282, 0.657280718}