4k^2+10k=8

Solution for 4k^2+10k=8 equation:

Simplifying
4k2 + 10k = 8

Reorder the terms:
10k + 4k2 = 8

Solving
10k + 4k2 = 8

Solving for variable 'k'.

Reorder the terms:
-8 + 10k + 4k2 = 8 + -8

Combine like terms: 8 + -8 = 0
-8 + 10k + 4k2 = 0

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

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

Simplifying
-4 + 5k + 2k2 = 0

Solving
-4 + 5k + 2k2 = 0

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

Divide each side by '2'.
-2 + 2.5k + k2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 2.5k + 2 + k2 = 0 + 2

Reorder the terms:
-2 + 2 + 2.5k + k2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 2.5k + k2 = 0 + 2
2.5k + k2 = 0 + 2

Combine like terms: 0 + 2 = 2
2.5k + k2 = 2

The k term is 2.5k.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5k + 1.5625 + k2 = 2 + 1.5625

Reorder the terms:
1.5625 + 2.5k + k2 = 2 + 1.5625

Combine like terms: 2 + 1.5625 = 3.5625
1.5625 + 2.5k + k2 = 3.5625

Factor a perfect square on the left side:
(k + 1.25)(k + 1.25) = 3.5625

Calculate the square root of the right side: 1.887458609

Break this problem into two subproblems by setting 
(k + 1.25) equal to 1.887458609 and -1.887458609.

Subproblem 1
k + 1.25 = 1.887458609

Simplifying
k + 1.25 = 1.887458609

Reorder the terms:
1.25 + k = 1.887458609

Solving
1.25 + k = 1.887458609

Solving for variable 'k'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + k = 1.887458609 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + k = 1.887458609 + -1.25
k = 1.887458609 + -1.25

Combine like terms: 1.887458609 + -1.25 = 0.637458609
k = 0.637458609

Simplifying
k = 0.637458609

Subproblem 2
k + 1.25 = -1.887458609

Simplifying
k + 1.25 = -1.887458609

Reorder the terms:
1.25 + k = -1.887458609

Solving
1.25 + k = -1.887458609

Solving for variable 'k'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + k = -1.887458609 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + k = -1.887458609 + -1.25
k = -1.887458609 + -1.25

Combine like terms: -1.887458609 + -1.25 = -3.137458609
k = -3.137458609

Simplifying
k = -3.137458609

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {0.637458609, -3.137458609}
Solution
k = {0.637458609, -3.137458609}