-40x^2+180x-196=0

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Solution for -40x^2+180x-196=0 equation: 


Simplifying
-40x2 + 180x + -196 = 0

Reorder the terms:
-196 + 180x + -40x2 = 0

Solving
-196 + 180x + -40x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-49 + 45x + -10x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-49 + 45x + -10x2)' equal to zero and attempt to solve:

Simplifying
-49 + 45x + -10x2 = 0

Solving
-49 + 45x + -10x2 = 0

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

Divide each side by '-10'.
4.9 + -4.5x + x2 = 0.0

Move the constant term to the right:

Add '-4.9' to each side of the equation.
4.9 + -4.5x + -4.9 + x2 = 0.0 + -4.9

Reorder the terms:
4.9 + -4.9 + -4.5x + x2 = 0.0 + -4.9

Combine like terms: 4.9 + -4.9 = 0.0
0.0 + -4.5x + x2 = 0.0 + -4.9
-4.5x + x2 = 0.0 + -4.9

Combine like terms: 0.0 + -4.9 = -4.9
-4.5x + x2 = -4.9

The x term is -4.5x.  Take half its coefficient (-2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
-4.5x + 5.0625 + x2 = -4.9 + 5.0625

Reorder the terms:
5.0625 + -4.5x + x2 = -4.9 + 5.0625

Combine like terms: -4.9 + 5.0625 = 0.1625
5.0625 + -4.5x + x2 = 0.1625

Factor a perfect square on the left side:
(x + -2.25)(x + -2.25) = 0.1625

Calculate the square root of the right side: 0.403112887

Break this problem into two subproblems by setting 
(x + -2.25) equal to 0.403112887 and -0.403112887.


Subproblem 1
x + -2.25 = 0.403112887

Simplifying
x + -2.25 = 0.403112887

Reorder the terms:
-2.25 + x = 0.403112887

Solving
-2.25 + x = 0.403112887

Solving for variable 'x'.

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

Add '2.25' to each side of the equation.
-2.25 + 2.25 + x = 0.403112887 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + x = 0.403112887 + 2.25
x = 0.403112887 + 2.25

Combine like terms: 0.403112887 + 2.25 = 2.653112887
x = 2.653112887

Simplifying
x = 2.653112887


Subproblem 2
x + -2.25 = -0.403112887

Simplifying
x + -2.25 = -0.403112887

Reorder the terms:
-2.25 + x = -0.403112887

Solving
-2.25 + x = -0.403112887

Solving for variable 'x'.

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

Add '2.25' to each side of the equation.
-2.25 + 2.25 + x = -0.403112887 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + x = -0.403112887 + 2.25
x = -0.403112887 + 2.25

Combine like terms: -0.403112887 + 2.25 = 1.846887113
x = 1.846887113

Simplifying
x = 1.846887113


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.653112887, 1.846887113}
Solution
x = {2.653112887, 1.846887113}

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