x^2+11-22=6x+2

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Solution for x^2+11-22=6x+2 equation:


Simplifying
x2 + 11 + -22 = 6x + 2

Reorder the terms:
11 + -22 + x2 = 6x + 2

Combine like terms: 11 + -22 = -11
-11 + x2 = 6x + 2

Reorder the terms:
-11 + x2 = 2 + 6x

Solving
-11 + x2 = 2 + 6x

Solving for variable 'x'.

Reorder the terms:
-11 + -2 + -6x + x2 = 2 + 6x + -2 + -6x

Combine like terms: -11 + -2 = -13
-13 + -6x + x2 = 2 + 6x + -2 + -6x

Reorder the terms:
-13 + -6x + x2 = 2 + -2 + 6x + -6x

Combine like terms: 2 + -2 = 0
-13 + -6x + x2 = 0 + 6x + -6x
-13 + -6x + x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-13 + -6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '13' to each side of the equation.
-13 + -6x + 13 + x2 = 0 + 13

Reorder the terms:
-13 + 13 + -6x + x2 = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -6x + x2 = 0 + 13
-6x + x2 = 0 + 13

Combine like terms: 0 + 13 = 13
-6x + x2 = 13

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = 13 + 9

Reorder the terms:
9 + -6x + x2 = 13 + 9

Combine like terms: 13 + 9 = 22
9 + -6x + x2 = 22

Factor a perfect square on the left side:
(x + -3)(x + -3) = 22

Calculate the square root of the right side: 4.69041576

Break this problem into two subproblems by setting 
(x + -3) equal to 4.69041576 and -4.69041576.


Subproblem 1
x + -3 = 4.69041576

Simplifying
x + -3 = 4.69041576

Reorder the terms:
-3 + x = 4.69041576

Solving
-3 + x = 4.69041576

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = 4.69041576 + 3

Combine like terms: -3 + 3 = 0
0 + x = 4.69041576 + 3
x = 4.69041576 + 3

Combine like terms: 4.69041576 + 3 = 7.69041576
x = 7.69041576

Simplifying
x = 7.69041576


Subproblem 2
x + -3 = -4.69041576

Simplifying
x + -3 = -4.69041576

Reorder the terms:
-3 + x = -4.69041576

Solving
-3 + x = -4.69041576

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = -4.69041576 + 3

Combine like terms: -3 + 3 = 0
0 + x = -4.69041576 + 3
x = -4.69041576 + 3

Combine like terms: -4.69041576 + 3 = -1.69041576
x = -1.69041576

Simplifying
x = -1.69041576


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.69041576, -1.69041576}

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