20x^2-22x=-3

Solution for 20x^2-22x=-3 equation:

Simplifying
20x2 + -22x = -3

Reorder the terms:
-22x + 20x2 = -3

Solving
-22x + 20x2 = -3

Solving for variable 'x'.

Reorder the terms:
3 + -22x + 20x2 = -3 + 3

Combine like terms: -3 + 3 = 0
3 + -22x + 20x2 = 0

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

Divide each side by '20'.
0.15 + -1.1x + x2 = 0

Move the constant term to the right:

Add '-0.15' to each side of the equation.
0.15 + -1.1x + -0.15 + x2 = 0 + -0.15

Reorder the terms:
0.15 + -0.15 + -1.1x + x2 = 0 + -0.15

Combine like terms: 0.15 + -0.15 = 0.00
0.00 + -1.1x + x2 = 0 + -0.15
-1.1x + x2 = 0 + -0.15

Combine like terms: 0 + -0.15 = -0.15
-1.1x + x2 = -0.15

The x term is -1.1x.  Take half its coefficient (-0.55).
Square it (0.3025) and add it to both sides.

Add '0.3025' to each side of the equation.
-1.1x + 0.3025 + x2 = -0.15 + 0.3025

Reorder the terms:
0.3025 + -1.1x + x2 = -0.15 + 0.3025

Combine like terms: -0.15 + 0.3025 = 0.1525
0.3025 + -1.1x + x2 = 0.1525

Factor a perfect square on the left side:
(x + -0.55)(x + -0.55) = 0.1525

Calculate the square root of the right side: 0.390512484

Break this problem into two subproblems by setting 
(x + -0.55) equal to 0.390512484 and -0.390512484.

Subproblem 1
x + -0.55 = 0.390512484

Simplifying
x + -0.55 = 0.390512484

Reorder the terms:
-0.55 + x = 0.390512484

Solving
-0.55 + x = 0.390512484

Solving for variable 'x'.

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

Add '0.55' to each side of the equation.
-0.55 + 0.55 + x = 0.390512484 + 0.55

Combine like terms: -0.55 + 0.55 = 0.00
0.00 + x = 0.390512484 + 0.55
x = 0.390512484 + 0.55

Combine like terms: 0.390512484 + 0.55 = 0.940512484
x = 0.940512484

Simplifying
x = 0.940512484

Subproblem 2
x + -0.55 = -0.390512484

Simplifying
x + -0.55 = -0.390512484

Reorder the terms:
-0.55 + x = -0.390512484

Solving
-0.55 + x = -0.390512484

Solving for variable 'x'.

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

Add '0.55' to each side of the equation.
-0.55 + 0.55 + x = -0.390512484 + 0.55

Combine like terms: -0.55 + 0.55 = 0.00
0.00 + x = -0.390512484 + 0.55
x = -0.390512484 + 0.55

Combine like terms: -0.390512484 + 0.55 = 0.159487516
x = 0.159487516

Simplifying
x = 0.159487516

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.940512484, 0.159487516}