16x=8x^2-15

Solution for 16x=8x^2-15 equation:

Simplifying
16x = 8x2 + -15

Reorder the terms:
16x = -15 + 8x2

Solving
16x = -15 + 8x2

Solving for variable 'x'.

Reorder the terms:
15 + 16x + -8x2 = -15 + 8x2 + 15 + -8x2

Reorder the terms:
15 + 16x + -8x2 = -15 + 15 + 8x2 + -8x2

Combine like terms: -15 + 15 = 0
15 + 16x + -8x2 = 0 + 8x2 + -8x2
15 + 16x + -8x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
15 + 16x + -8x2 = 0

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

Divide each side by '-8'.
-1.875 + -2x + x2 = 0

Move the constant term to the right:

Add '1.875' to each side of the equation.
-1.875 + -2x + 1.875 + x2 = 0 + 1.875

Reorder the terms:
-1.875 + 1.875 + -2x + x2 = 0 + 1.875

Combine like terms: -1.875 + 1.875 = 0.000
0.000 + -2x + x2 = 0 + 1.875
-2x + x2 = 0 + 1.875

Combine like terms: 0 + 1.875 = 1.875
-2x + x2 = 1.875

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 1.875 + 1

Reorder the terms:
1 + -2x + x2 = 1.875 + 1

Combine like terms: 1.875 + 1 = 2.875
1 + -2x + x2 = 2.875

Factor a perfect square on the left side:
(x + -1)(x + -1) = 2.875

Calculate the square root of the right side: 1.695582496

Break this problem into two subproblems by setting 
(x + -1) equal to 1.695582496 and -1.695582496.

Subproblem 1
x + -1 = 1.695582496

Simplifying
x + -1 = 1.695582496

Reorder the terms:
-1 + x = 1.695582496

Solving
-1 + x = 1.695582496

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 1.695582496 + 1

Combine like terms: -1 + 1 = 0
0 + x = 1.695582496 + 1
x = 1.695582496 + 1

Combine like terms: 1.695582496 + 1 = 2.695582496
x = 2.695582496

Simplifying
x = 2.695582496

Subproblem 2
x + -1 = -1.695582496

Simplifying
x + -1 = -1.695582496

Reorder the terms:
-1 + x = -1.695582496

Solving
-1 + x = -1.695582496

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -1.695582496 + 1

Combine like terms: -1 + 1 = 0
0 + x = -1.695582496 + 1
x = -1.695582496 + 1

Combine like terms: -1.695582496 + 1 = -0.695582496
x = -0.695582496

Simplifying
x = -0.695582496

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.695582496, -0.695582496}