15(17+x)=(x+8)(x+8)

Solution for 15(17+x)=(x+8)(x+8) equation:

Simplifying
15(17 + x) = (x + 8)(x + 8)
(17 * 15 + x * 15) = (x + 8)(x + 8)
(255 + 15x) = (x + 8)(x + 8)

Reorder the terms:
255 + 15x = (8 + x)(x + 8)

Reorder the terms:
255 + 15x = (8 + x)(8 + x)

Multiply (8 + x) * (8 + x)
255 + 15x = (8(8 + x) + x(8 + x))
255 + 15x = ((8 * 8 + x * 8) + x(8 + x))
255 + 15x = ((64 + 8x) + x(8 + x))
255 + 15x = (64 + 8x + (8 * x + x * x))
255 + 15x = (64 + 8x + (8x + x2))

Combine like terms: 8x + 8x = 16x
255 + 15x = (64 + 16x + x2)

Solving
255 + 15x = 64 + 16x + x2

Solving for variable 'x'.

Reorder the terms:
255 + -64 + 15x + -16x + -1x2 = 64 + 16x + x2 + -64 + -16x + -1x2

Combine like terms: 255 + -64 = 191
191 + 15x + -16x + -1x2 = 64 + 16x + x2 + -64 + -16x + -1x2

Combine like terms: 15x + -16x = -1x
191 + -1x + -1x2 = 64 + 16x + x2 + -64 + -16x + -1x2

Reorder the terms:
191 + -1x + -1x2 = 64 + -64 + 16x + -16x + x2 + -1x2

Combine like terms: 64 + -64 = 0
191 + -1x + -1x2 = 0 + 16x + -16x + x2 + -1x2
191 + -1x + -1x2 = 16x + -16x + x2 + -1x2

Combine like terms: 16x + -16x = 0
191 + -1x + -1x2 = 0 + x2 + -1x2
191 + -1x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
191 + -1x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-191 + x + x2 = 0

Move the constant term to the right:

Add '191' to each side of the equation.
-191 + x + 191 + x2 = 0 + 191

Reorder the terms:
-191 + 191 + x + x2 = 0 + 191

Combine like terms: -191 + 191 = 0
0 + x + x2 = 0 + 191
x + x2 = 0 + 191

Combine like terms: 0 + 191 = 191
x + x2 = 191

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + x2 = 191 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 191 + 0.25

Combine like terms: 191 + 0.25 = 191.25
1.25 + x2 = 191.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 191.25

Calculate the square root of the right side: 13.829316686

Break this problem into two subproblems by setting 
(x + 0.5) equal to 13.829316686 and -13.829316686.

Subproblem 1
x + 0.5 = 13.829316686

Simplifying
x + 0.5 = 13.829316686

Reorder the terms:
0.5 + x = 13.829316686

Solving
0.5 + x = 13.829316686

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 13.829316686 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 13.829316686 + -0.5
x = 13.829316686 + -0.5

Combine like terms: 13.829316686 + -0.5 = 13.329316686
x = 13.329316686

Simplifying
x = 13.329316686

Subproblem 2
x + 0.5 = -13.829316686

Simplifying
x + 0.5 = -13.829316686

Reorder the terms:
0.5 + x = -13.829316686

Solving
0.5 + x = -13.829316686

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -13.829316686 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -13.829316686 + -0.5
x = -13.829316686 + -0.5

Combine like terms: -13.829316686 + -0.5 = -14.329316686
x = -14.329316686

Simplifying
x = -14.329316686

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.329316686, -14.329316686}