9x+67=x^2+25x+25

Solution for 9x+67=x^2+25x+25 equation:

Simplifying
9x + 67 = x2 + 25x + 25

Reorder the terms:
67 + 9x = x2 + 25x + 25

Reorder the terms:
67 + 9x = 25 + 25x + x2

Solving
67 + 9x = 25 + 25x + x2

Solving for variable 'x'.

Reorder the terms:
67 + -25 + 9x + -25x + -1x2 = 25 + 25x + x2 + -25 + -25x + -1x2

Combine like terms: 67 + -25 = 42
42 + 9x + -25x + -1x2 = 25 + 25x + x2 + -25 + -25x + -1x2

Combine like terms: 9x + -25x = -16x
42 + -16x + -1x2 = 25 + 25x + x2 + -25 + -25x + -1x2

Reorder the terms:
42 + -16x + -1x2 = 25 + -25 + 25x + -25x + x2 + -1x2

Combine like terms: 25 + -25 = 0
42 + -16x + -1x2 = 0 + 25x + -25x + x2 + -1x2
42 + -16x + -1x2 = 25x + -25x + x2 + -1x2

Combine like terms: 25x + -25x = 0
42 + -16x + -1x2 = 0 + x2 + -1x2
42 + -16x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
42 + -16x + -1x2 = 0

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

Divide each side by '-1'.
-42 + 16x + x2 = 0

Move the constant term to the right:

Add '42' to each side of the equation.
-42 + 16x + 42 + x2 = 0 + 42

Reorder the terms:
-42 + 42 + 16x + x2 = 0 + 42

Combine like terms: -42 + 42 = 0
0 + 16x + x2 = 0 + 42
16x + x2 = 0 + 42

Combine like terms: 0 + 42 = 42
16x + x2 = 42

The x term is 16x.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16x + 64 + x2 = 42 + 64

Reorder the terms:
64 + 16x + x2 = 42 + 64

Combine like terms: 42 + 64 = 106
64 + 16x + x2 = 106

Factor a perfect square on the left side:
(x + 8)(x + 8) = 106

Calculate the square root of the right side: 10.295630141

Break this problem into two subproblems by setting 
(x + 8) equal to 10.295630141 and -10.295630141.

Subproblem 1
x + 8 = 10.295630141

Simplifying
x + 8 = 10.295630141

Reorder the terms:
8 + x = 10.295630141

Solving
8 + x = 10.295630141

Solving for variable 'x'.

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

Add '-8' to each side of the equation.
8 + -8 + x = 10.295630141 + -8

Combine like terms: 8 + -8 = 0
0 + x = 10.295630141 + -8
x = 10.295630141 + -8

Combine like terms: 10.295630141 + -8 = 2.295630141
x = 2.295630141

Simplifying
x = 2.295630141

Subproblem 2
x + 8 = -10.295630141

Simplifying
x + 8 = -10.295630141

Reorder the terms:
8 + x = -10.295630141

Solving
8 + x = -10.295630141

Solving for variable 'x'.

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

Add '-8' to each side of the equation.
8 + -8 + x = -10.295630141 + -8

Combine like terms: 8 + -8 = 0
0 + x = -10.295630141 + -8
x = -10.295630141 + -8

Combine like terms: -10.295630141 + -8 = -18.295630141
x = -18.295630141

Simplifying
x = -18.295630141

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.295630141, -18.295630141}