20x^2-2x-21=

Solution for 20x^2-2x-21= equation:

Simplifying
20x2 + -2x + -21 = 0

Reorder the terms:
-21 + -2x + 20x2 = 0

Solving
-21 + -2x + 20x2 = 0

Solving for variable 'x'.

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

Divide each side by '20'.
-1.05 + -0.1x + x2 = 0

Move the constant term to the right:

Add '1.05' to each side of the equation.
-1.05 + -0.1x + 1.05 + x2 = 0 + 1.05

Reorder the terms:
-1.05 + 1.05 + -0.1x + x2 = 0 + 1.05

Combine like terms: -1.05 + 1.05 = 0.00
0.00 + -0.1x + x2 = 0 + 1.05
-0.1x + x2 = 0 + 1.05

Combine like terms: 0 + 1.05 = 1.05
-0.1x + x2 = 1.05

The x term is -0.1x.  Take half its coefficient (-0.05).
Square it (0.0025) and add it to both sides.

Add '0.0025' to each side of the equation.
-0.1x + 0.0025 + x2 = 1.05 + 0.0025

Reorder the terms:
0.0025 + -0.1x + x2 = 1.05 + 0.0025

Combine like terms: 1.05 + 0.0025 = 1.0525
0.0025 + -0.1x + x2 = 1.0525

Factor a perfect square on the left side:
(x + -0.05)(x + -0.05) = 1.0525

Calculate the square root of the right side: 1.025914226

Break this problem into two subproblems by setting 
(x + -0.05) equal to 1.025914226 and -1.025914226.

Subproblem 1
x + -0.05 = 1.025914226

Simplifying
x + -0.05 = 1.025914226

Reorder the terms:
-0.05 + x = 1.025914226

Solving
-0.05 + x = 1.025914226

Solving for variable 'x'.

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

Add '0.05' to each side of the equation.
-0.05 + 0.05 + x = 1.025914226 + 0.05

Combine like terms: -0.05 + 0.05 = 0.00
0.00 + x = 1.025914226 + 0.05
x = 1.025914226 + 0.05

Combine like terms: 1.025914226 + 0.05 = 1.075914226
x = 1.075914226

Simplifying
x = 1.075914226

Subproblem 2
x + -0.05 = -1.025914226

Simplifying
x + -0.05 = -1.025914226

Reorder the terms:
-0.05 + x = -1.025914226

Solving
-0.05 + x = -1.025914226

Solving for variable 'x'.

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

Add '0.05' to each side of the equation.
-0.05 + 0.05 + x = -1.025914226 + 0.05

Combine like terms: -0.05 + 0.05 = 0.00
0.00 + x = -1.025914226 + 0.05
x = -1.025914226 + 0.05

Combine like terms: -1.025914226 + 0.05 = -0.975914226
x = -0.975914226

Simplifying
x = -0.975914226

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.075914226, -0.975914226}