x+9=4(x-1)(x-1)

Solution for x+9=4(x-1)(x-1) equation:

Simplifying
x + 9 = 4(x + -1)(x + -1)

Reorder the terms:
9 + x = 4(x + -1)(x + -1)

Reorder the terms:
9 + x = 4(-1 + x)(x + -1)

Reorder the terms:
9 + x = 4(-1 + x)(-1 + x)

Multiply (-1 + x) * (-1 + x)
9 + x = 4(-1(-1 + x) + x(-1 + x))
9 + x = 4((-1 * -1 + x * -1) + x(-1 + x))
9 + x = 4((1 + -1x) + x(-1 + x))
9 + x = 4(1 + -1x + (-1 * x + x * x))
9 + x = 4(1 + -1x + (-1x + x2))

Combine like terms: -1x + -1x = -2x
9 + x = 4(1 + -2x + x2)
9 + x = (1 * 4 + -2x * 4 + x2 * 4)
9 + x = (4 + -8x + 4x2)

Solving
9 + x = 4 + -8x + 4x2

Solving for variable 'x'.

Reorder the terms:
9 + -4 + x + 8x + -4x2 = 4 + -8x + 4x2 + -4 + 8x + -4x2

Combine like terms: 9 + -4 = 5
5 + x + 8x + -4x2 = 4 + -8x + 4x2 + -4 + 8x + -4x2

Combine like terms: x + 8x = 9x
5 + 9x + -4x2 = 4 + -8x + 4x2 + -4 + 8x + -4x2

Reorder the terms:
5 + 9x + -4x2 = 4 + -4 + -8x + 8x + 4x2 + -4x2

Combine like terms: 4 + -4 = 0
5 + 9x + -4x2 = 0 + -8x + 8x + 4x2 + -4x2
5 + 9x + -4x2 = -8x + 8x + 4x2 + -4x2

Combine like terms: -8x + 8x = 0
5 + 9x + -4x2 = 0 + 4x2 + -4x2
5 + 9x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
5 + 9x + -4x2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-1.25 + -2.25x + x2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + -2.25x + 1.25 + x2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + -2.25x + x2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + -2.25x + x2 = 0 + 1.25
-2.25x + x2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
-2.25x + x2 = 1.25

The x term is -2.25x.  Take half its coefficient (-1.125).
Square it (1.265625) and add it to both sides.

Add '1.265625' to each side of the equation.
-2.25x + 1.265625 + x2 = 1.25 + 1.265625

Reorder the terms:
1.265625 + -2.25x + x2 = 1.25 + 1.265625

Combine like terms: 1.25 + 1.265625 = 2.515625
1.265625 + -2.25x + x2 = 2.515625

Factor a perfect square on the left side:
(x + -1.125)(x + -1.125) = 2.515625

Calculate the square root of the right side: 1.586072193

Break this problem into two subproblems by setting 
(x + -1.125) equal to 1.586072193 and -1.586072193.

Subproblem 1
x + -1.125 = 1.586072193

Simplifying
x + -1.125 = 1.586072193

Reorder the terms:
-1.125 + x = 1.586072193

Solving
-1.125 + x = 1.586072193

Solving for variable 'x'.

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

Add '1.125' to each side of the equation.
-1.125 + 1.125 + x = 1.586072193 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + x = 1.586072193 + 1.125
x = 1.586072193 + 1.125

Combine like terms: 1.586072193 + 1.125 = 2.711072193
x = 2.711072193

Simplifying
x = 2.711072193

Subproblem 2
x + -1.125 = -1.586072193

Simplifying
x + -1.125 = -1.586072193

Reorder the terms:
-1.125 + x = -1.586072193

Solving
-1.125 + x = -1.586072193

Solving for variable 'x'.

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

Add '1.125' to each side of the equation.
-1.125 + 1.125 + x = -1.586072193 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + x = -1.586072193 + 1.125
x = -1.586072193 + 1.125

Combine like terms: -1.586072193 + 1.125 = -0.461072193
x = -0.461072193

Simplifying
x = -0.461072193

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.711072193, -0.461072193}