10x^2+6x+1=20

Solution for 10x^2+6x+1=20 equation:

Simplifying
10x2 + 6x + 1 = 20

Reorder the terms:
1 + 6x + 10x2 = 20

Solving
1 + 6x + 10x2 = 20

Solving for variable 'x'.

Reorder the terms:
1 + -20 + 6x + 10x2 = 20 + -20

Combine like terms: 1 + -20 = -19
-19 + 6x + 10x2 = 20 + -20

Combine like terms: 20 + -20 = 0
-19 + 6x + 10x2 = 0

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

Divide each side by '10'.
-1.9 + 0.6x + x2 = 0

Move the constant term to the right:

Add '1.9' to each side of the equation.
-1.9 + 0.6x + 1.9 + x2 = 0 + 1.9

Reorder the terms:
-1.9 + 1.9 + 0.6x + x2 = 0 + 1.9

Combine like terms: -1.9 + 1.9 = 0.0
0.0 + 0.6x + x2 = 0 + 1.9
0.6x + x2 = 0 + 1.9

Combine like terms: 0 + 1.9 = 1.9
0.6x + x2 = 1.9

The x term is 0.6x.  Take half its coefficient (0.3).
Square it (0.09) and add it to both sides.

Add '0.09' to each side of the equation.
0.6x + 0.09 + x2 = 1.9 + 0.09

Reorder the terms:
0.09 + 0.6x + x2 = 1.9 + 0.09

Combine like terms: 1.9 + 0.09 = 1.99
0.09 + 0.6x + x2 = 1.99

Factor a perfect square on the left side:
(x + 0.3)(x + 0.3) = 1.99

Calculate the square root of the right side: 1.410673598

Break this problem into two subproblems by setting 
(x + 0.3) equal to 1.410673598 and -1.410673598.

Subproblem 1
x + 0.3 = 1.410673598

Simplifying
x + 0.3 = 1.410673598

Reorder the terms:
0.3 + x = 1.410673598

Solving
0.3 + x = 1.410673598

Solving for variable 'x'.

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

Add '-0.3' to each side of the equation.
0.3 + -0.3 + x = 1.410673598 + -0.3

Combine like terms: 0.3 + -0.3 = 0.0
0.0 + x = 1.410673598 + -0.3
x = 1.410673598 + -0.3

Combine like terms: 1.410673598 + -0.3 = 1.110673598
x = 1.110673598

Simplifying
x = 1.110673598

Subproblem 2
x + 0.3 = -1.410673598

Simplifying
x + 0.3 = -1.410673598

Reorder the terms:
0.3 + x = -1.410673598

Solving
0.3 + x = -1.410673598

Solving for variable 'x'.

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

Add '-0.3' to each side of the equation.
0.3 + -0.3 + x = -1.410673598 + -0.3

Combine like terms: 0.3 + -0.3 = 0.0
0.0 + x = -1.410673598 + -0.3
x = -1.410673598 + -0.3

Combine like terms: -1.410673598 + -0.3 = -1.710673598
x = -1.710673598

Simplifying
x = -1.710673598

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.110673598, -1.710673598}