2x^2-22x+18=0

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


Simplifying
2x2 + -22x + 18 = 0

Reorder the terms:
18 + -22x + 2x2 = 0

Solving
18 + -22x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(9 + -11x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(9 + -11x + x2)' equal to zero and attempt to solve:

Simplifying
9 + -11x + x2 = 0

Solving
9 + -11x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + -11x + -9 + x2 = 0 + -9

Reorder the terms:
9 + -9 + -11x + x2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -11x + x2 = 0 + -9
-11x + x2 = 0 + -9

Combine like terms: 0 + -9 = -9
-11x + x2 = -9

The x term is -11x.  Take half its coefficient (-5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
-11x + 30.25 + x2 = -9 + 30.25

Reorder the terms:
30.25 + -11x + x2 = -9 + 30.25

Combine like terms: -9 + 30.25 = 21.25
30.25 + -11x + x2 = 21.25

Factor a perfect square on the left side:
(x + -5.5)(x + -5.5) = 21.25

Calculate the square root of the right side: 4.609772229

Break this problem into two subproblems by setting 
(x + -5.5) equal to 4.609772229 and -4.609772229.


Subproblem 1
x + -5.5 = 4.609772229

Simplifying
x + -5.5 = 4.609772229

Reorder the terms:
-5.5 + x = 4.609772229

Solving
-5.5 + x = 4.609772229

Solving for variable 'x'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + x = 4.609772229 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x = 4.609772229 + 5.5
x = 4.609772229 + 5.5

Combine like terms: 4.609772229 + 5.5 = 10.109772229
x = 10.109772229

Simplifying
x = 10.109772229


Subproblem 2
x + -5.5 = -4.609772229

Simplifying
x + -5.5 = -4.609772229

Reorder the terms:
-5.5 + x = -4.609772229

Solving
-5.5 + x = -4.609772229

Solving for variable 'x'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + x = -4.609772229 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x = -4.609772229 + 5.5
x = -4.609772229 + 5.5

Combine like terms: -4.609772229 + 5.5 = 0.890227771
x = 0.890227771

Simplifying
x = 0.890227771


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.109772229, 0.890227771}
Solution
x = {10.109772229, 0.890227771}

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