5x^2-10x=-2

Solution for 5x^2-10x=-2 equation:

Simplifying
5x2 + -10x = -2

Reorder the terms:
-10x + 5x2 = -2

Solving
-10x + 5x2 = -2

Solving for variable 'x'.

Reorder the terms:
2 + -10x + 5x2 = -2 + 2

Combine like terms: -2 + 2 = 0
2 + -10x + 5x2 = 0

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

Divide each side by '5'.
0.4 + -2x + x2 = 0

Move the constant term to the right:

Add '-0.4' to each side of the equation.
0.4 + -2x + -0.4 + x2 = 0 + -0.4

Reorder the terms:
0.4 + -0.4 + -2x + x2 = 0 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + -2x + x2 = 0 + -0.4
-2x + x2 = 0 + -0.4

Combine like terms: 0 + -0.4 = -0.4
-2x + x2 = -0.4

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = -0.4 + 1

Reorder the terms:
1 + -2x + x2 = -0.4 + 1

Combine like terms: -0.4 + 1 = 0.6
1 + -2x + x2 = 0.6

Factor a perfect square on the left side:
(x + -1)(x + -1) = 0.6

Calculate the square root of the right side: 0.774596669

Break this problem into two subproblems by setting 
(x + -1) equal to 0.774596669 and -0.774596669.

Subproblem 1
x + -1 = 0.774596669

Simplifying
x + -1 = 0.774596669

Reorder the terms:
-1 + x = 0.774596669

Solving
-1 + x = 0.774596669

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 0.774596669 + 1

Combine like terms: -1 + 1 = 0
0 + x = 0.774596669 + 1
x = 0.774596669 + 1

Combine like terms: 0.774596669 + 1 = 1.774596669
x = 1.774596669

Simplifying
x = 1.774596669

Subproblem 2
x + -1 = -0.774596669

Simplifying
x + -1 = -0.774596669

Reorder the terms:
-1 + x = -0.774596669

Solving
-1 + x = -0.774596669

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -0.774596669 + 1

Combine like terms: -1 + 1 = 0
0 + x = -0.774596669 + 1
x = -0.774596669 + 1

Combine like terms: -0.774596669 + 1 = 0.225403331
x = 0.225403331

Simplifying
x = 0.225403331

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.774596669, 0.225403331}