0=-56x^2+70x-6

Solution for 0=-56x^2+70x-6 equation:

Simplifying
0 = -56x2 + 70x + -6

Reorder the terms:
0 = -6 + 70x + -56x2

Solving
0 = -6 + 70x + -56x2

Solving for variable 'x'.

Combine like terms: 0 + 6 = 6
6 + -70x + 56x2 = -6 + 70x + -56x2 + 6 + -70x + 56x2

Reorder the terms:
6 + -70x + 56x2 = -6 + 6 + 70x + -70x + -56x2 + 56x2

Combine like terms: -6 + 6 = 0
6 + -70x + 56x2 = 0 + 70x + -70x + -56x2 + 56x2
6 + -70x + 56x2 = 70x + -70x + -56x2 + 56x2

Combine like terms: 70x + -70x = 0
6 + -70x + 56x2 = 0 + -56x2 + 56x2
6 + -70x + 56x2 = -56x2 + 56x2

Combine like terms: -56x2 + 56x2 = 0
6 + -70x + 56x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -35x + 28x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + -35x + 28x2)' equal to zero and attempt to solve:

Simplifying
3 + -35x + 28x2 = 0

Solving
3 + -35x + 28x2 = 0

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

Divide each side by '28'.
0.1071428571 + -1.25x + x2 = 0

Move the constant term to the right:

Add '-0.1071428571' to each side of the equation.
0.1071428571 + -1.25x + -0.1071428571 + x2 = 0 + -0.1071428571

Reorder the terms:
0.1071428571 + -0.1071428571 + -1.25x + x2 = 0 + -0.1071428571

Combine like terms: 0.1071428571 + -0.1071428571 = 0.0000000000
0.0000000000 + -1.25x + x2 = 0 + -0.1071428571
-1.25x + x2 = 0 + -0.1071428571

Combine like terms: 0 + -0.1071428571 = -0.1071428571
-1.25x + x2 = -0.1071428571

The x term is -1.25x.  Take half its coefficient (-0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
-1.25x + 0.390625 + x2 = -0.1071428571 + 0.390625

Reorder the terms:
0.390625 + -1.25x + x2 = -0.1071428571 + 0.390625

Combine like terms: -0.1071428571 + 0.390625 = 0.2834821429
0.390625 + -1.25x + x2 = 0.2834821429

Factor a perfect square on the left side:
(x + -0.625)(x + -0.625) = 0.2834821429

Calculate the square root of the right side: 0.532430411

Break this problem into two subproblems by setting 
(x + -0.625) equal to 0.532430411 and -0.532430411.

Subproblem 1
x + -0.625 = 0.532430411

Simplifying
x + -0.625 = 0.532430411

Reorder the terms:
-0.625 + x = 0.532430411

Solving
-0.625 + x = 0.532430411

Solving for variable 'x'.

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

Add '0.625' to each side of the equation.
-0.625 + 0.625 + x = 0.532430411 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + x = 0.532430411 + 0.625
x = 0.532430411 + 0.625

Combine like terms: 0.532430411 + 0.625 = 1.157430411
x = 1.157430411

Simplifying
x = 1.157430411

Subproblem 2
x + -0.625 = -0.532430411

Simplifying
x + -0.625 = -0.532430411

Reorder the terms:
-0.625 + x = -0.532430411

Solving
-0.625 + x = -0.532430411

Solving for variable 'x'.

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

Add '0.625' to each side of the equation.
-0.625 + 0.625 + x = -0.532430411 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + x = -0.532430411 + 0.625
x = -0.532430411 + 0.625

Combine like terms: -0.532430411 + 0.625 = 0.092569589
x = 0.092569589

Simplifying
x = 0.092569589

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.157430411, 0.092569589}
Solution
x = {1.157430411, 0.092569589}