4k^2-k-29=0

Solution for 4k^2-k-29=0 equation:

Simplifying
4k2 + -1k + -29 = 0

Reorder the terms:
-29 + -1k + 4k2 = 0

Solving
-29 + -1k + 4k2 = 0

Solving for variable 'k'.

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

Divide each side by '4'.
-7.25 + -0.25k + k2 = 0

Move the constant term to the right:

Add '7.25' to each side of the equation.
-7.25 + -0.25k + 7.25 + k2 = 0 + 7.25

Reorder the terms:
-7.25 + 7.25 + -0.25k + k2 = 0 + 7.25

Combine like terms: -7.25 + 7.25 = 0.00
0.00 + -0.25k + k2 = 0 + 7.25
-0.25k + k2 = 0 + 7.25

Combine like terms: 0 + 7.25 = 7.25
-0.25k + k2 = 7.25

The k term is -0.25k.  Take half its coefficient (-0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
-0.25k + 0.015625 + k2 = 7.25 + 0.015625

Reorder the terms:
0.015625 + -0.25k + k2 = 7.25 + 0.015625

Combine like terms: 7.25 + 0.015625 = 7.265625
0.015625 + -0.25k + k2 = 7.265625

Factor a perfect square on the left side:
(k + -0.125)(k + -0.125) = 7.265625

Calculate the square root of the right side: 2.695482332

Break this problem into two subproblems by setting 
(k + -0.125) equal to 2.695482332 and -2.695482332.

Subproblem 1
k + -0.125 = 2.695482332

Simplifying
k + -0.125 = 2.695482332

Reorder the terms:
-0.125 + k = 2.695482332

Solving
-0.125 + k = 2.695482332

Solving for variable 'k'.

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

Add '0.125' to each side of the equation.
-0.125 + 0.125 + k = 2.695482332 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + k = 2.695482332 + 0.125
k = 2.695482332 + 0.125

Combine like terms: 2.695482332 + 0.125 = 2.820482332
k = 2.820482332

Simplifying
k = 2.820482332

Subproblem 2
k + -0.125 = -2.695482332

Simplifying
k + -0.125 = -2.695482332

Reorder the terms:
-0.125 + k = -2.695482332

Solving
-0.125 + k = -2.695482332

Solving for variable 'k'.

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

Add '0.125' to each side of the equation.
-0.125 + 0.125 + k = -2.695482332 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + k = -2.695482332 + 0.125
k = -2.695482332 + 0.125

Combine like terms: -2.695482332 + 0.125 = -2.570482332
k = -2.570482332

Simplifying
k = -2.570482332

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {2.820482332, -2.570482332}