(x-3)(x+3)+11=10x

Solution for (x-3)(x+3)+11=10x equation:

Simplifying
(x + -3)(x + 3) + 11 = 10x

Reorder the terms:
(-3 + x)(x + 3) + 11 = 10x

Reorder the terms:
(-3 + x)(3 + x) + 11 = 10x

Multiply (-3 + x) * (3 + x)
(-3(3 + x) + x(3 + x)) + 11 = 10x
((3 * -3 + x * -3) + x(3 + x)) + 11 = 10x
((-9 + -3x) + x(3 + x)) + 11 = 10x
(-9 + -3x + (3 * x + x * x)) + 11 = 10x
(-9 + -3x + (3x + x2)) + 11 = 10x

Combine like terms: -3x + 3x = 0
(-9 + 0 + x2) + 11 = 10x
(-9 + x2) + 11 = 10x

Reorder the terms:
-9 + 11 + x2 = 10x

Combine like terms: -9 + 11 = 2
2 + x2 = 10x

Solving
2 + x2 = 10x

Solving for variable 'x'.

Reorder the terms:
2 + -10x + x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
2 + -10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -10x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + -10x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -10x + x2 = 0 + -2
-10x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-10x + x2 = -2

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = -2 + 25

Reorder the terms:
25 + -10x + x2 = -2 + 25

Combine like terms: -2 + 25 = 23
25 + -10x + x2 = 23

Factor a perfect square on the left side:
(x + -5)(x + -5) = 23

Calculate the square root of the right side: 4.795831523

Break this problem into two subproblems by setting 
(x + -5) equal to 4.795831523 and -4.795831523.

Subproblem 1
x + -5 = 4.795831523

Simplifying
x + -5 = 4.795831523

Reorder the terms:
-5 + x = 4.795831523

Solving
-5 + x = 4.795831523

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = 4.795831523 + 5

Combine like terms: -5 + 5 = 0
0 + x = 4.795831523 + 5
x = 4.795831523 + 5

Combine like terms: 4.795831523 + 5 = 9.795831523
x = 9.795831523

Simplifying
x = 9.795831523

Subproblem 2
x + -5 = -4.795831523

Simplifying
x + -5 = -4.795831523

Reorder the terms:
-5 + x = -4.795831523

Solving
-5 + x = -4.795831523

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = -4.795831523 + 5

Combine like terms: -5 + 5 = 0
0 + x = -4.795831523 + 5
x = -4.795831523 + 5

Combine like terms: -4.795831523 + 5 = 0.204168477
x = 0.204168477

Simplifying
x = 0.204168477

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.795831523, 0.204168477}