10x^2+20=100x^2-20x-3

Solution for 10x^2+20=100x^2-20x-3 equation:

Simplifying
10x2 + 20 = 100x2 + -20x + -3

Reorder the terms:
20 + 10x2 = 100x2 + -20x + -3

Reorder the terms:
20 + 10x2 = -3 + -20x + 100x2

Solving
20 + 10x2 = -3 + -20x + 100x2

Solving for variable 'x'.

Reorder the terms:
20 + 3 + 20x + 10x2 + -100x2 = -3 + -20x + 100x2 + 3 + 20x + -100x2

Combine like terms: 20 + 3 = 23
23 + 20x + 10x2 + -100x2 = -3 + -20x + 100x2 + 3 + 20x + -100x2

Combine like terms: 10x2 + -100x2 = -90x2
23 + 20x + -90x2 = -3 + -20x + 100x2 + 3 + 20x + -100x2

Reorder the terms:
23 + 20x + -90x2 = -3 + 3 + -20x + 20x + 100x2 + -100x2

Combine like terms: -3 + 3 = 0
23 + 20x + -90x2 = 0 + -20x + 20x + 100x2 + -100x2
23 + 20x + -90x2 = -20x + 20x + 100x2 + -100x2

Combine like terms: -20x + 20x = 0
23 + 20x + -90x2 = 0 + 100x2 + -100x2
23 + 20x + -90x2 = 100x2 + -100x2

Combine like terms: 100x2 + -100x2 = 0
23 + 20x + -90x2 = 0

Begin completing the square.  Divide all terms by
-90 the coefficient of the squared term: 

Divide each side by '-90'.
-0.2555555556 + -0.2222222222x + x2 = 0.0

Move the constant term to the right:

Add '0.2555555556' to each side of the equation.
-0.2555555556 + -0.2222222222x + 0.2555555556 + x2 = 0.0 + 0.2555555556

Reorder the terms:
-0.2555555556 + 0.2555555556 + -0.2222222222x + x2 = 0.0 + 0.2555555556

Combine like terms: -0.2555555556 + 0.2555555556 = 0.0000000000
0.0000000000 + -0.2222222222x + x2 = 0.0 + 0.2555555556
-0.2222222222x + x2 = 0.0 + 0.2555555556

Combine like terms: 0.0 + 0.2555555556 = 0.2555555556
-0.2222222222x + x2 = 0.2555555556

The x term is -0.2222222222x.  Take half its coefficient (-0.1111111111).
Square it (0.01234567901) and add it to both sides.

Add '0.01234567901' to each side of the equation.
-0.2222222222x + 0.01234567901 + x2 = 0.2555555556 + 0.01234567901

Reorder the terms:
0.01234567901 + -0.2222222222x + x2 = 0.2555555556 + 0.01234567901

Combine like terms: 0.2555555556 + 0.01234567901 = 0.26790123461
0.01234567901 + -0.2222222222x + x2 = 0.26790123461

Factor a perfect square on the left side:
(x + -0.1111111111)(x + -0.1111111111) = 0.26790123461

Calculate the square root of the right side: 0.517591764

Break this problem into two subproblems by setting 
(x + -0.1111111111) equal to 0.517591764 and -0.517591764.

Subproblem 1
x + -0.1111111111 = 0.517591764

Simplifying
x + -0.1111111111 = 0.517591764

Reorder the terms:
-0.1111111111 + x = 0.517591764

Solving
-0.1111111111 + x = 0.517591764

Solving for variable 'x'.

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

Add '0.1111111111' to each side of the equation.
-0.1111111111 + 0.1111111111 + x = 0.517591764 + 0.1111111111

Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000
0.0000000000 + x = 0.517591764 + 0.1111111111
x = 0.517591764 + 0.1111111111

Combine like terms: 0.517591764 + 0.1111111111 = 0.6287028751
x = 0.6287028751

Simplifying
x = 0.6287028751

Subproblem 2
x + -0.1111111111 = -0.517591764

Simplifying
x + -0.1111111111 = -0.517591764

Reorder the terms:
-0.1111111111 + x = -0.517591764

Solving
-0.1111111111 + x = -0.517591764

Solving for variable 'x'.

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

Add '0.1111111111' to each side of the equation.
-0.1111111111 + 0.1111111111 + x = -0.517591764 + 0.1111111111

Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000
0.0000000000 + x = -0.517591764 + 0.1111111111
x = -0.517591764 + 0.1111111111

Combine like terms: -0.517591764 + 0.1111111111 = -0.4064806529
x = -0.4064806529

Simplifying
x = -0.4064806529

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.6287028751, -0.4064806529}