10k^2+20k-95=-10

Solution for 10k^2+20k-95=-10 equation:

Simplifying
10k2 + 20k + -95 = -10

Reorder the terms:
-95 + 20k + 10k2 = -10

Solving
-95 + 20k + 10k2 = -10

Solving for variable 'k'.

Reorder the terms:
-95 + 10 + 20k + 10k2 = -10 + 10

Combine like terms: -95 + 10 = -85
-85 + 20k + 10k2 = -10 + 10

Combine like terms: -10 + 10 = 0
-85 + 20k + 10k2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-17 + 4k + 2k2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-17 + 4k + 2k2)' equal to zero and attempt to solve:

Simplifying
-17 + 4k + 2k2 = 0

Solving
-17 + 4k + 2k2 = 0

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

Divide each side by '2'.
-8.5 + 2k + k2 = 0

Move the constant term to the right:

Add '8.5' to each side of the equation.
-8.5 + 2k + 8.5 + k2 = 0 + 8.5

Reorder the terms:
-8.5 + 8.5 + 2k + k2 = 0 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + 2k + k2 = 0 + 8.5
2k + k2 = 0 + 8.5

Combine like terms: 0 + 8.5 = 8.5
2k + k2 = 8.5

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 = 8.5 + 1

Reorder the terms:
1 + 2k + k2 = 8.5 + 1

Combine like terms: 8.5 + 1 = 9.5
1 + 2k + k2 = 9.5

Factor a perfect square on the left side:
(k + 1)(k + 1) = 9.5

Calculate the square root of the right side: 3.082207001

Break this problem into two subproblems by setting 
(k + 1) equal to 3.082207001 and -3.082207001.

Subproblem 1
k + 1 = 3.082207001

Simplifying
k + 1 = 3.082207001

Reorder the terms:
1 + k = 3.082207001

Solving
1 + k = 3.082207001

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 = 3.082207001 + -1

Combine like terms: 1 + -1 = 0
0 + k = 3.082207001 + -1
k = 3.082207001 + -1

Combine like terms: 3.082207001 + -1 = 2.082207001
k = 2.082207001

Simplifying
k = 2.082207001

Subproblem 2
k + 1 = -3.082207001

Simplifying
k + 1 = -3.082207001

Reorder the terms:
1 + k = -3.082207001

Solving
1 + k = -3.082207001

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 = -3.082207001 + -1

Combine like terms: 1 + -1 = 0
0 + k = -3.082207001 + -1
k = -3.082207001 + -1

Combine like terms: -3.082207001 + -1 = -4.082207001
k = -4.082207001

Simplifying
k = -4.082207001

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {2.082207001, -4.082207001}
Solution
k = {2.082207001, -4.082207001}