-16x^2+56x-32=0

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Solution for -16x^2+56x-32=0 equation: 


Simplifying
-16x2 + 56x + -32 = 0

Reorder the terms:
-32 + 56x + -16x2 = 0

Solving
-32 + 56x + -16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8'.
8(-4 + 7x + -2x2) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(-4 + 7x + -2x2)' equal to zero and attempt to solve:

Simplifying
-4 + 7x + -2x2 = 0

Solving
-4 + 7x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
2 + -3.5x + x2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -3.5x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + -3.5x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3.5x + x2 = 0 + -2
-3.5x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-3.5x + x2 = -2

The x term is -3.5x.  Take half its coefficient (-1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
-3.5x + 3.0625 + x2 = -2 + 3.0625

Reorder the terms:
3.0625 + -3.5x + x2 = -2 + 3.0625

Combine like terms: -2 + 3.0625 = 1.0625
3.0625 + -3.5x + x2 = 1.0625

Factor a perfect square on the left side:
(x + -1.75)(x + -1.75) = 1.0625

Calculate the square root of the right side: 1.030776406

Break this problem into two subproblems by setting 
(x + -1.75) equal to 1.030776406 and -1.030776406.


Subproblem 1
x + -1.75 = 1.030776406

Simplifying
x + -1.75 = 1.030776406

Reorder the terms:
-1.75 + x = 1.030776406

Solving
-1.75 + x = 1.030776406

Solving for variable 'x'.

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

Add '1.75' to each side of the equation.
-1.75 + 1.75 + x = 1.030776406 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + x = 1.030776406 + 1.75
x = 1.030776406 + 1.75

Combine like terms: 1.030776406 + 1.75 = 2.780776406
x = 2.780776406

Simplifying
x = 2.780776406


Subproblem 2
x + -1.75 = -1.030776406

Simplifying
x + -1.75 = -1.030776406

Reorder the terms:
-1.75 + x = -1.030776406

Solving
-1.75 + x = -1.030776406

Solving for variable 'x'.

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

Add '1.75' to each side of the equation.
-1.75 + 1.75 + x = -1.030776406 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + x = -1.030776406 + 1.75
x = -1.030776406 + 1.75

Combine like terms: -1.030776406 + 1.75 = 0.719223594
x = 0.719223594

Simplifying
x = 0.719223594


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.780776406, 0.719223594}
Solution
x = {2.780776406, 0.719223594}

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