5k^2+2k-67=10

Solution for 5k^2+2k-67=10 equation:

Simplifying
5k2 + 2k + -67 = 10

Reorder the terms:
-67 + 2k + 5k2 = 10

Solving
-67 + 2k + 5k2 = 10

Solving for variable 'k'.

Reorder the terms:
-67 + -10 + 2k + 5k2 = 10 + -10

Combine like terms: -67 + -10 = -77
-77 + 2k + 5k2 = 10 + -10

Combine like terms: 10 + -10 = 0
-77 + 2k + 5k2 = 0

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

Divide each side by '5'.
-15.4 + 0.4k + k2 = 0

Move the constant term to the right:

Add '15.4' to each side of the equation.
-15.4 + 0.4k + 15.4 + k2 = 0 + 15.4

Reorder the terms:
-15.4 + 15.4 + 0.4k + k2 = 0 + 15.4

Combine like terms: -15.4 + 15.4 = 0.0
0.0 + 0.4k + k2 = 0 + 15.4
0.4k + k2 = 0 + 15.4

Combine like terms: 0 + 15.4 = 15.4
0.4k + k2 = 15.4

The k term is 0.4k.  Take half its coefficient (0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
0.4k + 0.04 + k2 = 15.4 + 0.04

Reorder the terms:
0.04 + 0.4k + k2 = 15.4 + 0.04

Combine like terms: 15.4 + 0.04 = 15.44
0.04 + 0.4k + k2 = 15.44

Factor a perfect square on the left side:
(k + 0.2)(k + 0.2) = 15.44

Calculate the square root of the right side: 3.929376541

Break this problem into two subproblems by setting 
(k + 0.2) equal to 3.929376541 and -3.929376541.

Subproblem 1
k + 0.2 = 3.929376541

Simplifying
k + 0.2 = 3.929376541

Reorder the terms:
0.2 + k = 3.929376541

Solving
0.2 + k = 3.929376541

Solving for variable 'k'.

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

Add '-0.2' to each side of the equation.
0.2 + -0.2 + k = 3.929376541 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + k = 3.929376541 + -0.2
k = 3.929376541 + -0.2

Combine like terms: 3.929376541 + -0.2 = 3.729376541
k = 3.729376541

Simplifying
k = 3.729376541

Subproblem 2
k + 0.2 = -3.929376541

Simplifying
k + 0.2 = -3.929376541

Reorder the terms:
0.2 + k = -3.929376541

Solving
0.2 + k = -3.929376541

Solving for variable 'k'.

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

Add '-0.2' to each side of the equation.
0.2 + -0.2 + k = -3.929376541 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + k = -3.929376541 + -0.2
k = -3.929376541 + -0.2

Combine like terms: -3.929376541 + -0.2 = -4.129376541
k = -4.129376541

Simplifying
k = -4.129376541

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {3.729376541, -4.129376541}