k^2+15k-25=0

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Solution for k^2+15k-25=0 equation: 


Simplifying
k2 + 15k + -25 = 0

Reorder the terms:
-25 + 15k + k2 = 0

Solving
-25 + 15k + k2 = 0

Solving for variable 'k'.

Begin completing the square.

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + 15k + 25 + k2 = 0 + 25

Reorder the terms:
-25 + 25 + 15k + k2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + 15k + k2 = 0 + 25
15k + k2 = 0 + 25

Combine like terms: 0 + 25 = 25
15k + k2 = 25

The k term is 15k.  Take half its coefficient (7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
15k + 56.25 + k2 = 25 + 56.25

Reorder the terms:
56.25 + 15k + k2 = 25 + 56.25

Combine like terms: 25 + 56.25 = 81.25
56.25 + 15k + k2 = 81.25

Factor a perfect square on the left side:
(k + 7.5)(k + 7.5) = 81.25

Calculate the square root of the right side: 9.013878189

Break this problem into two subproblems by setting 
(k + 7.5) equal to 9.013878189 and -9.013878189.


Subproblem 1
k + 7.5 = 9.013878189

Simplifying
k + 7.5 = 9.013878189

Reorder the terms:
7.5 + k = 9.013878189

Solving
7.5 + k = 9.013878189

Solving for variable 'k'.

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

Add '-7.5' to each side of the equation.
7.5 + -7.5 + k = 9.013878189 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + k = 9.013878189 + -7.5
k = 9.013878189 + -7.5

Combine like terms: 9.013878189 + -7.5 = 1.513878189
k = 1.513878189

Simplifying
k = 1.513878189


Subproblem 2
k + 7.5 = -9.013878189

Simplifying
k + 7.5 = -9.013878189

Reorder the terms:
7.5 + k = -9.013878189

Solving
7.5 + k = -9.013878189

Solving for variable 'k'.

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

Add '-7.5' to each side of the equation.
7.5 + -7.5 + k = -9.013878189 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + k = -9.013878189 + -7.5
k = -9.013878189 + -7.5

Combine like terms: -9.013878189 + -7.5 = -16.513878189
k = -16.513878189

Simplifying
k = -16.513878189


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {1.513878189, -16.513878189}

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