16x^2-10x=16

Solution for 16x^2-10x=16 equation:

Simplifying
16x2 + -10x = 16

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

Solving
-10x + 16x2 = 16

Solving for variable 'x'.

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

Combine like terms: 16 + -16 = 0
-16 + -10x + 16x2 = 0

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

Ignore the factor 2.
Subproblem 1
Set the factor '(-8 + -5x + 8x2)' equal to zero and attempt to solve:

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

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

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

Divide each side by '8'.
-1 + -0.625x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -0.625x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -0.625x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -0.625x + x2 = 0 + 1
-0.625x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-0.625x + x2 = 1

The x term is -0.625x.  Take half its coefficient (-0.3125).
Square it (0.09765625) and add it to both sides.

Add '0.09765625' to each side of the equation.
-0.625x + 0.09765625 + x2 = 1 + 0.09765625

Reorder the terms:
0.09765625 + -0.625x + x2 = 1 + 0.09765625

Combine like terms: 1 + 0.09765625 = 1.09765625
0.09765625 + -0.625x + x2 = 1.09765625

Factor a perfect square on the left side:
(x + -0.3125)(x + -0.3125) = 1.09765625

Calculate the square root of the right side: 1.047690913

Break this problem into two subproblems by setting 
(x + -0.3125) equal to 1.047690913 and -1.047690913.

Subproblem 1
x + -0.3125 = 1.047690913

Simplifying
x + -0.3125 = 1.047690913

Reorder the terms:
-0.3125 + x = 1.047690913

Solving
-0.3125 + x = 1.047690913

Solving for variable 'x'.

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

Add '0.3125' to each side of the equation.
-0.3125 + 0.3125 + x = 1.047690913 + 0.3125

Combine like terms: -0.3125 + 0.3125 = 0.0000
0.0000 + x = 1.047690913 + 0.3125
x = 1.047690913 + 0.3125

Combine like terms: 1.047690913 + 0.3125 = 1.360190913
x = 1.360190913

Simplifying
x = 1.360190913

Subproblem 2
x + -0.3125 = -1.047690913

Simplifying
x + -0.3125 = -1.047690913

Reorder the terms:
-0.3125 + x = -1.047690913

Solving
-0.3125 + x = -1.047690913

Solving for variable 'x'.

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

Add '0.3125' to each side of the equation.
-0.3125 + 0.3125 + x = -1.047690913 + 0.3125

Combine like terms: -0.3125 + 0.3125 = 0.0000
0.0000 + x = -1.047690913 + 0.3125
x = -1.047690913 + 0.3125

Combine like terms: -1.047690913 + 0.3125 = -0.735190913
x = -0.735190913

Simplifying
x = -0.735190913

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.360190913, -0.735190913}
Solution
x = {1.360190913, -0.735190913}