100x^2-20x=-1

Solution for 100x^2-20x=-1 equation:

Simplifying
100x2 + -20x = -1

Reorder the terms:
-20x + 100x2 = -1

Solving
-20x + 100x2 = -1

Solving for variable 'x'.

Reorder the terms:
1 + -20x + 100x2 = -1 + 1

Combine like terms: -1 + 1 = 0
1 + -20x + 100x2 = 0

Factor a trinomial.
(1 + -10x)(1 + -10x) = 0

Subproblem 1
Set the factor '(1 + -10x)' equal to zero and attempt to solve:

Simplifying
1 + -10x = 0

Solving
1 + -10x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -10x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -10x = 0 + -1
-10x = 0 + -1

Combine like terms: 0 + -1 = -1
-10x = -1

Divide each side by '-10'.
x = 0.1

Simplifying
x = 0.1
Subproblem 2
Set the factor '(1 + -10x)' equal to zero and attempt to solve:

Simplifying
1 + -10x = 0

Solving
1 + -10x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -10x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -10x = 0 + -1
-10x = 0 + -1

Combine like terms: 0 + -1 = -1
-10x = -1

Divide each side by '-10'.
x = 0.1

Simplifying
x = 0.1
Solution
x = {0.1, 0.1}