x^2-22x+24=0

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Solution for x^2-22x+24=0 equation: 


Simplifying
x2 + -22x + 24 = 0

Reorder the terms:
24 + -22x + x2 = 0

Solving
24 + -22x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-24' to each side of the equation.
24 + -22x + -24 + x2 = 0 + -24

Reorder the terms:
24 + -24 + -22x + x2 = 0 + -24

Combine like terms: 24 + -24 = 0
0 + -22x + x2 = 0 + -24
-22x + x2 = 0 + -24

Combine like terms: 0 + -24 = -24
-22x + x2 = -24

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 = -24 + 121

Reorder the terms:
121 + -22x + x2 = -24 + 121

Combine like terms: -24 + 121 = 97
121 + -22x + x2 = 97

Factor a perfect square on the left side:
(x + -11)(x + -11) = 97

Calculate the square root of the right side: 9.848857802

Break this problem into two subproblems by setting 
(x + -11) equal to 9.848857802 and -9.848857802.


Subproblem 1
x + -11 = 9.848857802

Simplifying
x + -11 = 9.848857802

Reorder the terms:
-11 + x = 9.848857802

Solving
-11 + x = 9.848857802

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 = 9.848857802 + 11

Combine like terms: -11 + 11 = 0
0 + x = 9.848857802 + 11
x = 9.848857802 + 11

Combine like terms: 9.848857802 + 11 = 20.848857802
x = 20.848857802

Simplifying
x = 20.848857802


Subproblem 2
x + -11 = -9.848857802

Simplifying
x + -11 = -9.848857802

Reorder the terms:
-11 + x = -9.848857802

Solving
-11 + x = -9.848857802

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 = -9.848857802 + 11

Combine like terms: -11 + 11 = 0
0 + x = -9.848857802 + 11
x = -9.848857802 + 11

Combine like terms: -9.848857802 + 11 = 1.151142198
x = 1.151142198

Simplifying
x = 1.151142198


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {20.848857802, 1.151142198}

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