20x^2=x+2

Solution for 20x^2=x+2 equation:

Simplifying
20x2 = x + 2

Reorder the terms:
20x2 = 2 + x

Solving
20x2 = 2 + x

Solving for variable 'x'.

Reorder the terms:
-2 + -1x + 20x2 = 2 + x + -2 + -1x

Reorder the terms:
-2 + -1x + 20x2 = 2 + -2 + x + -1x

Combine like terms: 2 + -2 = 0
-2 + -1x + 20x2 = 0 + x + -1x
-2 + -1x + 20x2 = x + -1x

Combine like terms: x + -1x = 0
-2 + -1x + 20x2 = 0

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

Divide each side by '20'.
-0.1 + -0.05x + x2 = 0

Move the constant term to the right:

Add '0.1' to each side of the equation.
-0.1 + -0.05x + 0.1 + x2 = 0 + 0.1

Reorder the terms:
-0.1 + 0.1 + -0.05x + x2 = 0 + 0.1

Combine like terms: -0.1 + 0.1 = 0.0
0.0 + -0.05x + x2 = 0 + 0.1
-0.05x + x2 = 0 + 0.1

Combine like terms: 0 + 0.1 = 0.1
-0.05x + x2 = 0.1

The x term is -0.05x.  Take half its coefficient (-0.025).
Square it (0.000625) and add it to both sides.

Add '0.000625' to each side of the equation.
-0.05x + 0.000625 + x2 = 0.1 + 0.000625

Reorder the terms:
0.000625 + -0.05x + x2 = 0.1 + 0.000625

Combine like terms: 0.1 + 0.000625 = 0.100625
0.000625 + -0.05x + x2 = 0.100625

Factor a perfect square on the left side:
(x + -0.025)(x + -0.025) = 0.100625

Calculate the square root of the right side: 0.317214439

Break this problem into two subproblems by setting 
(x + -0.025) equal to 0.317214439 and -0.317214439.

Subproblem 1
x + -0.025 = 0.317214439

Simplifying
x + -0.025 = 0.317214439

Reorder the terms:
-0.025 + x = 0.317214439

Solving
-0.025 + x = 0.317214439

Solving for variable 'x'.

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

Add '0.025' to each side of the equation.
-0.025 + 0.025 + x = 0.317214439 + 0.025

Combine like terms: -0.025 + 0.025 = 0.000
0.000 + x = 0.317214439 + 0.025
x = 0.317214439 + 0.025

Combine like terms: 0.317214439 + 0.025 = 0.342214439
x = 0.342214439

Simplifying
x = 0.342214439

Subproblem 2
x + -0.025 = -0.317214439

Simplifying
x + -0.025 = -0.317214439

Reorder the terms:
-0.025 + x = -0.317214439

Solving
-0.025 + x = -0.317214439

Solving for variable 'x'.

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

Add '0.025' to each side of the equation.
-0.025 + 0.025 + x = -0.317214439 + 0.025

Combine like terms: -0.025 + 0.025 = 0.000
0.000 + x = -0.317214439 + 0.025
x = -0.317214439 + 0.025

Combine like terms: -0.317214439 + 0.025 = -0.292214439
x = -0.292214439

Simplifying
x = -0.292214439

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.342214439, -0.292214439}