20k^2-3k-35=1

Solution for 20k^2-3k-35=1 equation:

Simplifying
20k2 + -3k + -35 = 1

Reorder the terms:
-35 + -3k + 20k2 = 1

Solving
-35 + -3k + 20k2 = 1

Solving for variable 'k'.

Reorder the terms:
-35 + -1 + -3k + 20k2 = 1 + -1

Combine like terms: -35 + -1 = -36
-36 + -3k + 20k2 = 1 + -1

Combine like terms: 1 + -1 = 0
-36 + -3k + 20k2 = 0

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

Divide each side by '20'.
-1.8 + -0.15k + k2 = 0

Move the constant term to the right:

Add '1.8' to each side of the equation.
-1.8 + -0.15k + 1.8 + k2 = 0 + 1.8

Reorder the terms:
-1.8 + 1.8 + -0.15k + k2 = 0 + 1.8

Combine like terms: -1.8 + 1.8 = 0.0
0.0 + -0.15k + k2 = 0 + 1.8
-0.15k + k2 = 0 + 1.8

Combine like terms: 0 + 1.8 = 1.8
-0.15k + k2 = 1.8

The k term is -0.15k.  Take half its coefficient (-0.075).
Square it (0.005625) and add it to both sides.

Add '0.005625' to each side of the equation.
-0.15k + 0.005625 + k2 = 1.8 + 0.005625

Reorder the terms:
0.005625 + -0.15k + k2 = 1.8 + 0.005625

Combine like terms: 1.8 + 0.005625 = 1.805625
0.005625 + -0.15k + k2 = 1.805625

Factor a perfect square on the left side:
(k + -0.075)(k + -0.075) = 1.805625

Calculate the square root of the right side: 1.343735465

Break this problem into two subproblems by setting 
(k + -0.075) equal to 1.343735465 and -1.343735465.

Subproblem 1
k + -0.075 = 1.343735465

Simplifying
k + -0.075 = 1.343735465

Reorder the terms:
-0.075 + k = 1.343735465

Solving
-0.075 + k = 1.343735465

Solving for variable 'k'.

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

Add '0.075' to each side of the equation.
-0.075 + 0.075 + k = 1.343735465 + 0.075

Combine like terms: -0.075 + 0.075 = 0.000
0.000 + k = 1.343735465 + 0.075
k = 1.343735465 + 0.075

Combine like terms: 1.343735465 + 0.075 = 1.418735465
k = 1.418735465

Simplifying
k = 1.418735465

Subproblem 2
k + -0.075 = -1.343735465

Simplifying
k + -0.075 = -1.343735465

Reorder the terms:
-0.075 + k = -1.343735465

Solving
-0.075 + k = -1.343735465

Solving for variable 'k'.

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

Add '0.075' to each side of the equation.
-0.075 + 0.075 + k = -1.343735465 + 0.075

Combine like terms: -0.075 + 0.075 = 0.000
0.000 + k = -1.343735465 + 0.075
k = -1.343735465 + 0.075

Combine like terms: -1.343735465 + 0.075 = -1.268735465
k = -1.268735465

Simplifying
k = -1.268735465

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {1.418735465, -1.268735465}