-16x^2+40x-10=0

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Solution for -16x^2+40x-10=0 equation: 


Simplifying
-16x2 + 40x + -10 = 0

Reorder the terms:
-10 + 40x + -16x2 = 0

Solving
-10 + 40x + -16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 20x + -8x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-5 + 20x + -8x2)' equal to zero and attempt to solve:

Simplifying
-5 + 20x + -8x2 = 0

Solving
-5 + 20x + -8x2 = 0

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
0.625 + -2.5x + x2 = 0

Move the constant term to the right:

Add '-0.625' to each side of the equation.
0.625 + -2.5x + -0.625 + x2 = 0 + -0.625

Reorder the terms:
0.625 + -0.625 + -2.5x + x2 = 0 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + -2.5x + x2 = 0 + -0.625
-2.5x + x2 = 0 + -0.625

Combine like terms: 0 + -0.625 = -0.625
-2.5x + x2 = -0.625

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 = -0.625 + 1.5625

Reorder the terms:
1.5625 + -2.5x + x2 = -0.625 + 1.5625

Combine like terms: -0.625 + 1.5625 = 0.9375
1.5625 + -2.5x + x2 = 0.9375

Factor a perfect square on the left side:
(x + -1.25)(x + -1.25) = 0.9375

Calculate the square root of the right side: 0.968245837

Break this problem into two subproblems by setting 
(x + -1.25) equal to 0.968245837 and -0.968245837.


Subproblem 1
x + -1.25 = 0.968245837

Simplifying
x + -1.25 = 0.968245837

Reorder the terms:
-1.25 + x = 0.968245837

Solving
-1.25 + x = 0.968245837

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 = 0.968245837 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + x = 0.968245837 + 1.25
x = 0.968245837 + 1.25

Combine like terms: 0.968245837 + 1.25 = 2.218245837
x = 2.218245837

Simplifying
x = 2.218245837


Subproblem 2
x + -1.25 = -0.968245837

Simplifying
x + -1.25 = -0.968245837

Reorder the terms:
-1.25 + x = -0.968245837

Solving
-1.25 + x = -0.968245837

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 = -0.968245837 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + x = -0.968245837 + 1.25
x = -0.968245837 + 1.25

Combine like terms: -0.968245837 + 1.25 = 0.281754163
x = 0.281754163

Simplifying
x = 0.281754163


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.218245837, 0.281754163}
Solution
x = {2.218245837, 0.281754163}

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