15(x+8)+15=2x(x+8)

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Solution for 15(x+8)+15=2x(x+8) equation:


Simplifying
15(x + 8) + 15 = 2x(x + 8)

Reorder the terms:
15(8 + x) + 15 = 2x(x + 8)
(8 * 15 + x * 15) + 15 = 2x(x + 8)
(120 + 15x) + 15 = 2x(x + 8)

Reorder the terms:
120 + 15 + 15x = 2x(x + 8)

Combine like terms: 120 + 15 = 135
135 + 15x = 2x(x + 8)

Reorder the terms:
135 + 15x = 2x(8 + x)
135 + 15x = (8 * 2x + x * 2x)
135 + 15x = (16x + 2x2)

Solving
135 + 15x = 16x + 2x2

Solving for variable 'x'.

Combine like terms: 15x + -16x = -1x
135 + -1x + -2x2 = 16x + 2x2 + -16x + -2x2

Reorder the terms:
135 + -1x + -2x2 = 16x + -16x + 2x2 + -2x2

Combine like terms: 16x + -16x = 0
135 + -1x + -2x2 = 0 + 2x2 + -2x2
135 + -1x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
135 + -1x + -2x2 = 0

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

Divide each side by '-2'.
-67.5 + 0.5x + x2 = 0

Move the constant term to the right:

Add '67.5' to each side of the equation.
-67.5 + 0.5x + 67.5 + x2 = 0 + 67.5

Reorder the terms:
-67.5 + 67.5 + 0.5x + x2 = 0 + 67.5

Combine like terms: -67.5 + 67.5 = 0.0
0.0 + 0.5x + x2 = 0 + 67.5
0.5x + x2 = 0 + 67.5

Combine like terms: 0 + 67.5 = 67.5
0.5x + x2 = 67.5

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = 67.5 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 67.5 + 0.0625

Combine like terms: 67.5 + 0.0625 = 67.5625
0.0625 + 0.5x + x2 = 67.5625

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 67.5625

Calculate the square root of the right side: 8.219641111

Break this problem into two subproblems by setting 
(x + 0.25) equal to 8.219641111 and -8.219641111.

Subproblem 1

x + 0.25 = 8.219641111 Simplifying x + 0.25 = 8.219641111 Reorder the terms: 0.25 + x = 8.219641111 Solving 0.25 + x = 8.219641111 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 8.219641111 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 8.219641111 + -0.25 x = 8.219641111 + -0.25 Combine like terms: 8.219641111 + -0.25 = 7.969641111 x = 7.969641111 Simplifying x = 7.969641111

Subproblem 2

x + 0.25 = -8.219641111 Simplifying x + 0.25 = -8.219641111 Reorder the terms: 0.25 + x = -8.219641111 Solving 0.25 + x = -8.219641111 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -8.219641111 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -8.219641111 + -0.25 x = -8.219641111 + -0.25 Combine like terms: -8.219641111 + -0.25 = -8.469641111 x = -8.469641111 Simplifying x = -8.469641111

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.969641111, -8.469641111}

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