56.25k^2+1215k+45=0

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Solution for 56.25k^2+1215k+45=0 equation:


Simplifying
56.25k2 + 1215k + 45 = 0

Reorder the terms:
45 + 1215k + 56.25k2 = 0

Solving
45 + 1215k + 56.25k2 = 0

Solving for variable 'k'.

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

Divide each side by '56.25'.
0.8 + 21.6k + k2 = 0

Move the constant term to the right:

Add '-0.8' to each side of the equation.
0.8 + 21.6k + -0.8 + k2 = 0 + -0.8

Reorder the terms:
0.8 + -0.8 + 21.6k + k2 = 0 + -0.8

Combine like terms: 0.8 + -0.8 = 0.0
0.0 + 21.6k + k2 = 0 + -0.8
21.6k + k2 = 0 + -0.8

Combine like terms: 0 + -0.8 = -0.8
21.6k + k2 = -0.8

The k term is 21.6k.  Take half its coefficient (10.8).
Square it (116.64) and add it to both sides.

Add '116.64' to each side of the equation.
21.6k + 116.64 + k2 = -0.8 + 116.64

Reorder the terms:
116.64 + 21.6k + k2 = -0.8 + 116.64

Combine like terms: -0.8 + 116.64 = 115.84
116.64 + 21.6k + k2 = 115.84

Factor a perfect square on the left side:
(k + 10.8)(k + 10.8) = 115.84

Calculate the square root of the right side: 10.762899238

Break this problem into two subproblems by setting 
(k + 10.8) equal to 10.762899238 and -10.762899238.


Subproblem 1
k + 10.8 = 10.762899238

Simplifying
k + 10.8 = 10.762899238

Reorder the terms:
10.8 + k = 10.762899238

Solving
10.8 + k = 10.762899238

Solving for variable 'k'.

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

Add '-10.8' to each side of the equation.
10.8 + -10.8 + k = 10.762899238 + -10.8

Combine like terms: 10.8 + -10.8 = 0.0
0.0 + k = 10.762899238 + -10.8
k = 10.762899238 + -10.8

Combine like terms: 10.762899238 + -10.8 = -0.037100762
k = -0.037100762

Simplifying
k = -0.037100762


Subproblem 2
k + 10.8 = -10.762899238

Simplifying
k + 10.8 = -10.762899238

Reorder the terms:
10.8 + k = -10.762899238

Solving
10.8 + k = -10.762899238

Solving for variable 'k'.

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

Add '-10.8' to each side of the equation.
10.8 + -10.8 + k = -10.762899238 + -10.8

Combine like terms: 10.8 + -10.8 = 0.0
0.0 + k = -10.762899238 + -10.8
k = -10.762899238 + -10.8

Combine like terms: -10.762899238 + -10.8 = -21.562899238
k = -21.562899238

Simplifying
k = -21.562899238


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {-0.037100762, -21.562899238}

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