4k^2+8k-9=-0

Solution for 4k^2+8k-9=-0 equation:

Simplifying
4k2 + 8k + -9 = 0

Reorder the terms:
-9 + 8k + 4k2 = 0

Solving
-9 + 8k + 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 + 2k + k2 = 0

Move the constant term to the right:

Add '2.25' to each side of the equation.
-2.25 + 2k + 2.25 + k2 = 0 + 2.25

Reorder the terms:
-2.25 + 2.25 + 2k + k2 = 0 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + 2k + k2 = 0 + 2.25
2k + k2 = 0 + 2.25

Combine like terms: 0 + 2.25 = 2.25
2k + k2 = 2.25

The k term is 2k.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2k + 1 + k2 = 2.25 + 1

Reorder the terms:
1 + 2k + k2 = 2.25 + 1

Combine like terms: 2.25 + 1 = 3.25
1 + 2k + k2 = 3.25

Factor a perfect square on the left side:
(k + 1)(k + 1) = 3.25

Calculate the square root of the right side: 1.802775638

Break this problem into two subproblems by setting 
(k + 1) equal to 1.802775638 and -1.802775638.

Subproblem 1
k + 1 = 1.802775638

Simplifying
k + 1 = 1.802775638

Reorder the terms:
1 + k = 1.802775638

Solving
1 + k = 1.802775638

Solving for variable 'k'.

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

Add '-1' to each side of the equation.
1 + -1 + k = 1.802775638 + -1

Combine like terms: 1 + -1 = 0
0 + k = 1.802775638 + -1
k = 1.802775638 + -1

Combine like terms: 1.802775638 + -1 = 0.802775638
k = 0.802775638

Simplifying
k = 0.802775638

Subproblem 2
k + 1 = -1.802775638

Simplifying
k + 1 = -1.802775638

Reorder the terms:
1 + k = -1.802775638

Solving
1 + k = -1.802775638

Solving for variable 'k'.

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

Add '-1' to each side of the equation.
1 + -1 + k = -1.802775638 + -1

Combine like terms: 1 + -1 = 0
0 + k = -1.802775638 + -1
k = -1.802775638 + -1

Combine like terms: -1.802775638 + -1 = -2.802775638
k = -2.802775638

Simplifying
k = -2.802775638

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {0.802775638, -2.802775638}