140x^2-182x-56=0

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Solution for 140x^2-182x-56=0 equation: 


Simplifying
140x2 + -182x + -56 = 0

Reorder the terms:
-56 + -182x + 140x2 = 0

Solving
-56 + -182x + 140x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '14'.
14(-4 + -13x + 10x2) = 0

Ignore the factor 14.

Subproblem 1
Set the factor '(-4 + -13x + 10x2)' equal to zero and attempt to solve:

Simplifying
-4 + -13x + 10x2 = 0

Solving
-4 + -13x + 10x2 = 0

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

Divide each side by '10'.
-0.4 + -1.3x + x2 = 0.0

Move the constant term to the right:

Add '0.4' to each side of the equation.
-0.4 + -1.3x + 0.4 + x2 = 0.0 + 0.4

Reorder the terms:
-0.4 + 0.4 + -1.3x + x2 = 0.0 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + -1.3x + x2 = 0.0 + 0.4
-1.3x + x2 = 0.0 + 0.4

Combine like terms: 0.0 + 0.4 = 0.4
-1.3x + x2 = 0.4

The x term is -1.3x.  Take half its coefficient (-0.65).
Square it (0.4225) and add it to both sides.

Add '0.4225' to each side of the equation.
-1.3x + 0.4225 + x2 = 0.4 + 0.4225

Reorder the terms:
0.4225 + -1.3x + x2 = 0.4 + 0.4225

Combine like terms: 0.4 + 0.4225 = 0.8225
0.4225 + -1.3x + x2 = 0.8225

Factor a perfect square on the left side:
(x + -0.65)(x + -0.65) = 0.8225

Calculate the square root of the right side: 0.906917857

Break this problem into two subproblems by setting 
(x + -0.65) equal to 0.906917857 and -0.906917857.


Subproblem 1
x + -0.65 = 0.906917857

Simplifying
x + -0.65 = 0.906917857

Reorder the terms:
-0.65 + x = 0.906917857

Solving
-0.65 + x = 0.906917857

Solving for variable 'x'.

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

Add '0.65' to each side of the equation.
-0.65 + 0.65 + x = 0.906917857 + 0.65

Combine like terms: -0.65 + 0.65 = 0.00
0.00 + x = 0.906917857 + 0.65
x = 0.906917857 + 0.65

Combine like terms: 0.906917857 + 0.65 = 1.556917857
x = 1.556917857

Simplifying
x = 1.556917857


Subproblem 2
x + -0.65 = -0.906917857

Simplifying
x + -0.65 = -0.906917857

Reorder the terms:
-0.65 + x = -0.906917857

Solving
-0.65 + x = -0.906917857

Solving for variable 'x'.

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

Add '0.65' to each side of the equation.
-0.65 + 0.65 + x = -0.906917857 + 0.65

Combine like terms: -0.65 + 0.65 = 0.00
0.00 + x = -0.906917857 + 0.65
x = -0.906917857 + 0.65

Combine like terms: -0.906917857 + 0.65 = -0.256917857
x = -0.256917857

Simplifying
x = -0.256917857


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.556917857, -0.256917857}
Solution
x = {1.556917857, -0.256917857}

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