4x^2+10x-10=0

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

Simplifying
4x2 + 10x + -10 = 0

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

Solving
-10 + 10x + 4x2 = 0

Solving for variable 'x'.

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

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

Simplifying
-5 + 5x + 2x2 = 0

Solving
-5 + 5x + 2x2 = 0

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

Divide each side by '2'.
-2.5 + 2.5x + x2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + 2.5x + 2.5 + x2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + 2.5x + x2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + 2.5x + x2 = 0 + 2.5
2.5x + x2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
2.5x + x2 = 2.5

The x term is 2.5x.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x + 1.5625 + x2 = 2.5 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = 2.5 + 1.5625

Combine like terms: 2.5 + 1.5625 = 4.0625
1.5625 + 2.5x + x2 = 4.0625

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 4.0625

Calculate the square root of the right side: 2.015564437

Break this problem into two subproblems by setting 
(x + 1.25) equal to 2.015564437 and -2.015564437.

Subproblem 1
x + 1.25 = 2.015564437

Simplifying
x + 1.25 = 2.015564437

Reorder the terms:
1.25 + x = 2.015564437

Solving
1.25 + x = 2.015564437

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = 2.015564437 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = 2.015564437 + -1.25
x = 2.015564437 + -1.25

Combine like terms: 2.015564437 + -1.25 = 0.765564437
x = 0.765564437

Simplifying
x = 0.765564437

Subproblem 2
x + 1.25 = -2.015564437

Simplifying
x + 1.25 = -2.015564437

Reorder the terms:
1.25 + x = -2.015564437

Solving
1.25 + x = -2.015564437

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = -2.015564437 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = -2.015564437 + -1.25
x = -2.015564437 + -1.25

Combine like terms: -2.015564437 + -1.25 = -3.265564437
x = -3.265564437

Simplifying
x = -3.265564437

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.765564437, -3.265564437}
Solution
x = {0.765564437, -3.265564437}