-140x^2+44x+7=0

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Solution for -140x^2+44x+7=0 equation: 


Simplifying
-140x2 + 44x + 7 = 0

Reorder the terms:
7 + 44x + -140x2 = 0

Solving
7 + 44x + -140x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-140 the coefficient of the squared term: 

Divide each side by '-140'.
-0.05 + -0.3142857143x + x2 = 0

Move the constant term to the right:

Add '0.05' to each side of the equation.
-0.05 + -0.3142857143x + 0.05 + x2 = 0 + 0.05

Reorder the terms:
-0.05 + 0.05 + -0.3142857143x + x2 = 0 + 0.05

Combine like terms: -0.05 + 0.05 = 0.00
0.00 + -0.3142857143x + x2 = 0 + 0.05
-0.3142857143x + x2 = 0 + 0.05

Combine like terms: 0 + 0.05 = 0.05
-0.3142857143x + x2 = 0.05

The x term is -0.3142857143x.  Take half its coefficient (-0.1571428572).
Square it (0.02469387757) and add it to both sides.

Add '0.02469387757' to each side of the equation.
-0.3142857143x + 0.02469387757 + x2 = 0.05 + 0.02469387757

Reorder the terms:
0.02469387757 + -0.3142857143x + x2 = 0.05 + 0.02469387757

Combine like terms: 0.05 + 0.02469387757 = 0.07469387757
0.02469387757 + -0.3142857143x + x2 = 0.07469387757

Factor a perfect square on the left side:
(x + -0.1571428572)(x + -0.1571428572) = 0.07469387757

Calculate the square root of the right side: 0.273301807

Break this problem into two subproblems by setting 
(x + -0.1571428572) equal to 0.273301807 and -0.273301807.


Subproblem 1
x + -0.1571428572 = 0.273301807

Simplifying
x + -0.1571428572 = 0.273301807

Reorder the terms:
-0.1571428572 + x = 0.273301807

Solving
-0.1571428572 + x = 0.273301807

Solving for variable 'x'.

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

Add '0.1571428572' to each side of the equation.
-0.1571428572 + 0.1571428572 + x = 0.273301807 + 0.1571428572

Combine like terms: -0.1571428572 + 0.1571428572 = 0.0000000000
0.0000000000 + x = 0.273301807 + 0.1571428572
x = 0.273301807 + 0.1571428572

Combine like terms: 0.273301807 + 0.1571428572 = 0.4304446642
x = 0.4304446642

Simplifying
x = 0.4304446642


Subproblem 2
x + -0.1571428572 = -0.273301807

Simplifying
x + -0.1571428572 = -0.273301807

Reorder the terms:
-0.1571428572 + x = -0.273301807

Solving
-0.1571428572 + x = -0.273301807

Solving for variable 'x'.

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

Add '0.1571428572' to each side of the equation.
-0.1571428572 + 0.1571428572 + x = -0.273301807 + 0.1571428572

Combine like terms: -0.1571428572 + 0.1571428572 = 0.0000000000
0.0000000000 + x = -0.273301807 + 0.1571428572
x = -0.273301807 + 0.1571428572

Combine like terms: -0.273301807 + 0.1571428572 = -0.1161589498
x = -0.1161589498

Simplifying
x = -0.1161589498


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.4304446642, -0.1161589498}

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