5k^2+5k-3=

Solution for 5k^2+5k-3= equation:

Simplifying
5k2 + 5k + -3 = 0

Reorder the terms:
-3 + 5k + 5k2 = 0

Solving
-3 + 5k + 5k2 = 0

Solving for variable 'k'.

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

Divide each side by '5'.
-0.6 + k + k2 = 0

Move the constant term to the right:

Add '0.6' to each side of the equation.
-0.6 + k + 0.6 + k2 = 0 + 0.6

Reorder the terms:
-0.6 + 0.6 + k + k2 = 0 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + k + k2 = 0 + 0.6
k + k2 = 0 + 0.6

Combine like terms: 0 + 0.6 = 0.6
k + k2 = 0.6

The k term is k.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + k2 = 0.6 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + k2 = 0.6 + 0.25

Combine like terms: 0.6 + 0.25 = 0.85
1.25 + k2 = 0.85

Factor a perfect square on the left side:
(k + 0.5)(k + 0.5) = 0.85

Calculate the square root of the right side: 0.921954446

Break this problem into two subproblems by setting 
(k + 0.5) equal to 0.921954446 and -0.921954446.

Subproblem 1
k + 0.5 = 0.921954446

Simplifying
k + 0.5 = 0.921954446

Reorder the terms:
0.5 + k = 0.921954446

Solving
0.5 + k = 0.921954446

Solving for variable 'k'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + k = 0.921954446 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + k = 0.921954446 + -0.5
k = 0.921954446 + -0.5

Combine like terms: 0.921954446 + -0.5 = 0.421954446
k = 0.421954446

Simplifying
k = 0.421954446

Subproblem 2
k + 0.5 = -0.921954446

Simplifying
k + 0.5 = -0.921954446

Reorder the terms:
0.5 + k = -0.921954446

Solving
0.5 + k = -0.921954446

Solving for variable 'k'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + k = -0.921954446 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + k = -0.921954446 + -0.5
k = -0.921954446 + -0.5

Combine like terms: -0.921954446 + -0.5 = -1.421954446
k = -1.421954446

Simplifying
k = -1.421954446

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {0.421954446, -1.421954446}