-16x^2+64x-26=0

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Solution for -16x^2+64x-26=0 equation: 


Simplifying
-16x2 + 64x + -26 = 0

Reorder the terms:
-26 + 64x + -16x2 = 0

Solving
-26 + 64x + -16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-13 + 32x + -8x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-13 + 32x + -8x2)' equal to zero and attempt to solve:

Simplifying
-13 + 32x + -8x2 = 0

Solving
-13 + 32x + -8x2 = 0

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

Divide each side by '-8'.
1.625 + -4x + x2 = 0

Move the constant term to the right:

Add '-1.625' to each side of the equation.
1.625 + -4x + -1.625 + x2 = 0 + -1.625

Reorder the terms:
1.625 + -1.625 + -4x + x2 = 0 + -1.625

Combine like terms: 1.625 + -1.625 = 0.000
0.000 + -4x + x2 = 0 + -1.625
-4x + x2 = 0 + -1.625

Combine like terms: 0 + -1.625 = -1.625
-4x + x2 = -1.625

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = -1.625 + 4

Reorder the terms:
4 + -4x + x2 = -1.625 + 4

Combine like terms: -1.625 + 4 = 2.375
4 + -4x + x2 = 2.375

Factor a perfect square on the left side:
(x + -2)(x + -2) = 2.375

Calculate the square root of the right side: 1.541103501

Break this problem into two subproblems by setting 
(x + -2) equal to 1.541103501 and -1.541103501.


Subproblem 1
x + -2 = 1.541103501

Simplifying
x + -2 = 1.541103501

Reorder the terms:
-2 + x = 1.541103501

Solving
-2 + x = 1.541103501

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 1.541103501 + 2

Combine like terms: -2 + 2 = 0
0 + x = 1.541103501 + 2
x = 1.541103501 + 2

Combine like terms: 1.541103501 + 2 = 3.541103501
x = 3.541103501

Simplifying
x = 3.541103501


Subproblem 2
x + -2 = -1.541103501

Simplifying
x + -2 = -1.541103501

Reorder the terms:
-2 + x = -1.541103501

Solving
-2 + x = -1.541103501

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -1.541103501 + 2

Combine like terms: -2 + 2 = 0
0 + x = -1.541103501 + 2
x = -1.541103501 + 2

Combine like terms: -1.541103501 + 2 = 0.458896499
x = 0.458896499

Simplifying
x = 0.458896499


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.541103501, 0.458896499}
Solution
x = {3.541103501, 0.458896499}

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