4k^2-1k-9=0

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Solution for 4k^2-1k-9=0 equation: 


Simplifying
4k2 + -1k + -9 = 0

Reorder the terms:
-9 + -1k + 4k2 = 0

Solving
-9 + -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'.
-2.25 + -0.25k + k2 = 0

Move the constant term to the right:

Add '2.25' to each side of the equation.
-2.25 + -0.25k + 2.25 + k2 = 0 + 2.25

Reorder the terms:
-2.25 + 2.25 + -0.25k + k2 = 0 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + -0.25k + k2 = 0 + 2.25
-0.25k + k2 = 0 + 2.25

Combine like terms: 0 + 2.25 = 2.25
-0.25k + k2 = 2.25

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 = 2.25 + 0.015625

Reorder the terms:
0.015625 + -0.25k + k2 = 2.25 + 0.015625

Combine like terms: 2.25 + 0.015625 = 2.265625
0.015625 + -0.25k + k2 = 2.265625

Factor a perfect square on the left side:
(k + -0.125)(k + -0.125) = 2.265625

Calculate the square root of the right side: 1.505199322

Break this problem into two subproblems by setting 
(k + -0.125) equal to 1.505199322 and -1.505199322.


Subproblem 1
k + -0.125 = 1.505199322

Simplifying
k + -0.125 = 1.505199322

Reorder the terms:
-0.125 + k = 1.505199322

Solving
-0.125 + k = 1.505199322

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 = 1.505199322 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + k = 1.505199322 + 0.125
k = 1.505199322 + 0.125

Combine like terms: 1.505199322 + 0.125 = 1.630199322
k = 1.630199322

Simplifying
k = 1.630199322


Subproblem 2
k + -0.125 = -1.505199322

Simplifying
k + -0.125 = -1.505199322

Reorder the terms:
-0.125 + k = -1.505199322

Solving
-0.125 + k = -1.505199322

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 = -1.505199322 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + k = -1.505199322 + 0.125
k = -1.505199322 + 0.125

Combine like terms: -1.505199322 + 0.125 = -1.380199322
k = -1.380199322

Simplifying
k = -1.380199322


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {1.630199322, -1.380199322}

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