x^2-22x+18=0

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Solution for x^2-22x+18=0 equation: 


Simplifying
x2 + -22x + 18 = 0

Reorder the terms:
18 + -22x + x2 = 0

Solving
18 + -22x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-18' to each side of the equation.
18 + -22x + -18 + x2 = 0 + -18

Reorder the terms:
18 + -18 + -22x + x2 = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -22x + x2 = 0 + -18
-22x + x2 = 0 + -18

Combine like terms: 0 + -18 = -18
-22x + x2 = -18

The x term is -22x.  Take half its coefficient (-11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
-22x + 121 + x2 = -18 + 121

Reorder the terms:
121 + -22x + x2 = -18 + 121

Combine like terms: -18 + 121 = 103
121 + -22x + x2 = 103

Factor a perfect square on the left side:
(x + -11)(x + -11) = 103

Calculate the square root of the right side: 10.148891565

Break this problem into two subproblems by setting 
(x + -11) equal to 10.148891565 and -10.148891565.


Subproblem 1
x + -11 = 10.148891565

Simplifying
x + -11 = 10.148891565

Reorder the terms:
-11 + x = 10.148891565

Solving
-11 + x = 10.148891565

Solving for variable 'x'.

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

Add '11' to each side of the equation.
-11 + 11 + x = 10.148891565 + 11

Combine like terms: -11 + 11 = 0
0 + x = 10.148891565 + 11
x = 10.148891565 + 11

Combine like terms: 10.148891565 + 11 = 21.148891565
x = 21.148891565

Simplifying
x = 21.148891565


Subproblem 2
x + -11 = -10.148891565

Simplifying
x + -11 = -10.148891565

Reorder the terms:
-11 + x = -10.148891565

Solving
-11 + x = -10.148891565

Solving for variable 'x'.

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

Add '11' to each side of the equation.
-11 + 11 + x = -10.148891565 + 11

Combine like terms: -11 + 11 = 0
0 + x = -10.148891565 + 11
x = -10.148891565 + 11

Combine like terms: -10.148891565 + 11 = 0.851108435
x = 0.851108435

Simplifying
x = 0.851108435


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {21.148891565, 0.851108435}

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