10x^2+4x+20=100x^2-20

Solution for 10x^2+4x+20=100x^2-20 equation:

Simplifying
10x2 + 4x + 20 = 100x2 + -20

Reorder the terms:
20 + 4x + 10x2 = 100x2 + -20

Reorder the terms:
20 + 4x + 10x2 = -20 + 100x2

Solving
20 + 4x + 10x2 = -20 + 100x2

Solving for variable 'x'.

Reorder the terms:
20 + 20 + 4x + 10x2 + -100x2 = -20 + 100x2 + 20 + -100x2

Combine like terms: 20 + 20 = 40
40 + 4x + 10x2 + -100x2 = -20 + 100x2 + 20 + -100x2

Combine like terms: 10x2 + -100x2 = -90x2
40 + 4x + -90x2 = -20 + 100x2 + 20 + -100x2

Reorder the terms:
40 + 4x + -90x2 = -20 + 20 + 100x2 + -100x2

Combine like terms: -20 + 20 = 0
40 + 4x + -90x2 = 0 + 100x2 + -100x2
40 + 4x + -90x2 = 100x2 + -100x2

Combine like terms: 100x2 + -100x2 = 0
40 + 4x + -90x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(20 + 2x + -45x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(20 + 2x + -45x2)' equal to zero and attempt to solve:

Simplifying
20 + 2x + -45x2 = 0

Solving
20 + 2x + -45x2 = 0

Begin completing the square.  Divide all terms by
-45 the coefficient of the squared term: 

Divide each side by '-45'.
-0.4444444444 + -0.04444444444x + x2 = 0

Move the constant term to the right:

Add '0.4444444444' to each side of the equation.
-0.4444444444 + -0.04444444444x + 0.4444444444 + x2 = 0 + 0.4444444444

Reorder the terms:
-0.4444444444 + 0.4444444444 + -0.04444444444x + x2 = 0 + 0.4444444444

Combine like terms: -0.4444444444 + 0.4444444444 = 0.0000000000
0.0000000000 + -0.04444444444x + x2 = 0 + 0.4444444444
-0.04444444444x + x2 = 0 + 0.4444444444

Combine like terms: 0 + 0.4444444444 = 0.4444444444
-0.04444444444x + x2 = 0.4444444444

The x term is -0.04444444444x.  Take half its coefficient (-0.02222222222).
Square it (0.0004938271604) and add it to both sides.

Add '0.0004938271604' to each side of the equation.
-0.04444444444x + 0.0004938271604 + x2 = 0.4444444444 + 0.0004938271604

Reorder the terms:
0.0004938271604 + -0.04444444444x + x2 = 0.4444444444 + 0.0004938271604

Combine like terms: 0.4444444444 + 0.0004938271604 = 0.4449382715604
0.0004938271604 + -0.04444444444x + x2 = 0.4449382715604

Factor a perfect square on the left side:
(x + -0.02222222222)(x + -0.02222222222) = 0.4449382715604

Calculate the square root of the right side: 0.667036934

Break this problem into two subproblems by setting 
(x + -0.02222222222) equal to 0.667036934 and -0.667036934.

Subproblem 1
x + -0.02222222222 = 0.667036934

Simplifying
x + -0.02222222222 = 0.667036934

Reorder the terms:
-0.02222222222 + x = 0.667036934

Solving
-0.02222222222 + x = 0.667036934

Solving for variable 'x'.

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

Add '0.02222222222' to each side of the equation.
-0.02222222222 + 0.02222222222 + x = 0.667036934 + 0.02222222222

Combine like terms: -0.02222222222 + 0.02222222222 = 0.00000000000
0.00000000000 + x = 0.667036934 + 0.02222222222
x = 0.667036934 + 0.02222222222

Combine like terms: 0.667036934 + 0.02222222222 = 0.68925915622
x = 0.68925915622

Simplifying
x = 0.68925915622

Subproblem 2
x + -0.02222222222 = -0.667036934

Simplifying
x + -0.02222222222 = -0.667036934

Reorder the terms:
-0.02222222222 + x = -0.667036934

Solving
-0.02222222222 + x = -0.667036934

Solving for variable 'x'.

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

Add '0.02222222222' to each side of the equation.
-0.02222222222 + 0.02222222222 + x = -0.667036934 + 0.02222222222

Combine like terms: -0.02222222222 + 0.02222222222 = 0.00000000000
0.00000000000 + x = -0.667036934 + 0.02222222222
x = -0.667036934 + 0.02222222222

Combine like terms: -0.667036934 + 0.02222222222 = -0.64481471178
x = -0.64481471178

Simplifying
x = -0.64481471178

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.68925915622, -0.64481471178}
Solution
x = {0.68925915622, -0.64481471178}