x+9=(x+9)(x+9)+7(x+9)-8

Solution for x+9=(x+9)(x+9)+7(x+9)-8 equation:

Simplifying
x + 9 = (x + 9)(x + 9) + 7(x + 9) + -8

Reorder the terms:
9 + x = (x + 9)(x + 9) + 7(x + 9) + -8

Reorder the terms:
9 + x = (9 + x)(x + 9) + 7(x + 9) + -8

Reorder the terms:
9 + x = (9 + x)(9 + x) + 7(x + 9) + -8

Multiply (9 + x) * (9 + x)
9 + x = (9(9 + x) + x(9 + x)) + 7(x + 9) + -8
9 + x = ((9 * 9 + x * 9) + x(9 + x)) + 7(x + 9) + -8
9 + x = ((81 + 9x) + x(9 + x)) + 7(x + 9) + -8
9 + x = (81 + 9x + (9 * x + x * x)) + 7(x + 9) + -8
9 + x = (81 + 9x + (9x + x2)) + 7(x + 9) + -8

Combine like terms: 9x + 9x = 18x
9 + x = (81 + 18x + x2) + 7(x + 9) + -8

Reorder the terms:
9 + x = 81 + 18x + x2 + 7(9 + x) + -8
9 + x = 81 + 18x + x2 + (9 * 7 + x * 7) + -8
9 + x = 81 + 18x + x2 + (63 + 7x) + -8

Reorder the terms:
9 + x = 81 + 63 + -8 + 18x + 7x + x2

Combine like terms: 81 + 63 = 144
9 + x = 144 + -8 + 18x + 7x + x2

Combine like terms: 144 + -8 = 136
9 + x = 136 + 18x + 7x + x2

Combine like terms: 18x + 7x = 25x
9 + x = 136 + 25x + x2

Solving
9 + x = 136 + 25x + x2

Solving for variable 'x'.

Reorder the terms:
9 + -136 + x + -25x + -1x2 = 136 + 25x + x2 + -136 + -25x + -1x2

Combine like terms: 9 + -136 = -127
-127 + x + -25x + -1x2 = 136 + 25x + x2 + -136 + -25x + -1x2

Combine like terms: x + -25x = -24x
-127 + -24x + -1x2 = 136 + 25x + x2 + -136 + -25x + -1x2

Reorder the terms:
-127 + -24x + -1x2 = 136 + -136 + 25x + -25x + x2 + -1x2

Combine like terms: 136 + -136 = 0
-127 + -24x + -1x2 = 0 + 25x + -25x + x2 + -1x2
-127 + -24x + -1x2 = 25x + -25x + x2 + -1x2

Combine like terms: 25x + -25x = 0
-127 + -24x + -1x2 = 0 + x2 + -1x2
-127 + -24x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-127 + -24x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(127 + 24x + x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(127 + 24x + x2)' equal to zero and attempt to solve:

Simplifying
127 + 24x + x2 = 0

Solving
127 + 24x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-127' to each side of the equation.
127 + 24x + -127 + x2 = 0 + -127

Reorder the terms:
127 + -127 + 24x + x2 = 0 + -127

Combine like terms: 127 + -127 = 0
0 + 24x + x2 = 0 + -127
24x + x2 = 0 + -127

Combine like terms: 0 + -127 = -127
24x + x2 = -127

The x term is 24x.  Take half its coefficient (12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
24x + 144 + x2 = -127 + 144

Reorder the terms:
144 + 24x + x2 = -127 + 144

Combine like terms: -127 + 144 = 17
144 + 24x + x2 = 17

Factor a perfect square on the left side:
(x + 12)(x + 12) = 17

Calculate the square root of the right side: 4.123105626

Break this problem into two subproblems by setting 
(x + 12) equal to 4.123105626 and -4.123105626.

Subproblem 1
x + 12 = 4.123105626

Simplifying
x + 12 = 4.123105626

Reorder the terms:
12 + x = 4.123105626

Solving
12 + x = 4.123105626

Solving for variable 'x'.

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

Add '-12' to each side of the equation.
12 + -12 + x = 4.123105626 + -12

Combine like terms: 12 + -12 = 0
0 + x = 4.123105626 + -12
x = 4.123105626 + -12

Combine like terms: 4.123105626 + -12 = -7.876894374
x = -7.876894374

Simplifying
x = -7.876894374

Subproblem 2
x + 12 = -4.123105626

Simplifying
x + 12 = -4.123105626

Reorder the terms:
12 + x = -4.123105626

Solving
12 + x = -4.123105626

Solving for variable 'x'.

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

Add '-12' to each side of the equation.
12 + -12 + x = -4.123105626 + -12

Combine like terms: 12 + -12 = 0
0 + x = -4.123105626 + -12
x = -4.123105626 + -12

Combine like terms: -4.123105626 + -12 = -16.123105626
x = -16.123105626

Simplifying
x = -16.123105626

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-7.876894374, -16.123105626}
Solution
x = {-7.876894374, -16.123105626}