10x^2+4x-2=0

Solution for 10x^2+4x-2=0 equation:

Simplifying
10x2 + 4x + -2 = 0

Reorder the terms:
-2 + 4x + 10x2 = 0

Solving
-2 + 4x + 10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + 2x + 5x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + 2x + 5x2)' equal to zero and attempt to solve:

Simplifying
-1 + 2x + 5x2 = 0

Solving
-1 + 2x + 5x2 = 0

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

Divide each side by '5'.
-0.2 + 0.4x + x2 = 0

Move the constant term to the right:

Add '0.2' to each side of the equation.
-0.2 + 0.4x + 0.2 + x2 = 0 + 0.2

Reorder the terms:
-0.2 + 0.2 + 0.4x + x2 = 0 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + 0.4x + x2 = 0 + 0.2
0.4x + x2 = 0 + 0.2

Combine like terms: 0 + 0.2 = 0.2
0.4x + x2 = 0.2

The x term is 0.4x.  Take half its coefficient (0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
0.4x + 0.04 + x2 = 0.2 + 0.04

Reorder the terms:
0.04 + 0.4x + x2 = 0.2 + 0.04

Combine like terms: 0.2 + 0.04 = 0.24
0.04 + 0.4x + x2 = 0.24

Factor a perfect square on the left side:
(x + 0.2)(x + 0.2) = 0.24

Calculate the square root of the right side: 0.489897949

Break this problem into two subproblems by setting 
(x + 0.2) equal to 0.489897949 and -0.489897949.

Subproblem 1
x + 0.2 = 0.489897949

Simplifying
x + 0.2 = 0.489897949

Reorder the terms:
0.2 + x = 0.489897949

Solving
0.2 + x = 0.489897949

Solving for variable 'x'.

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

Add '-0.2' to each side of the equation.
0.2 + -0.2 + x = 0.489897949 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + x = 0.489897949 + -0.2
x = 0.489897949 + -0.2

Combine like terms: 0.489897949 + -0.2 = 0.289897949
x = 0.289897949

Simplifying
x = 0.289897949

Subproblem 2
x + 0.2 = -0.489897949

Simplifying
x + 0.2 = -0.489897949

Reorder the terms:
0.2 + x = -0.489897949

Solving
0.2 + x = -0.489897949

Solving for variable 'x'.

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

Add '-0.2' to each side of the equation.
0.2 + -0.2 + x = -0.489897949 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + x = -0.489897949 + -0.2
x = -0.489897949 + -0.2

Combine like terms: -0.489897949 + -0.2 = -0.689897949
x = -0.689897949

Simplifying
x = -0.689897949

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.289897949, -0.689897949}
Solution
x = {0.289897949, -0.689897949}