2x^2+22=20x

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Solution for 2x^2+22=20x equation:


Simplifying
2x2 + 22 = 20x

Reorder the terms:
22 + 2x2 = 20x

Solving
22 + 2x2 = 20x

Solving for variable 'x'.

Reorder the terms:
22 + -20x + 2x2 = 20x + -20x

Combine like terms: 20x + -20x = 0
22 + -20x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(11 + -10x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(11 + -10x + x2)' equal to zero and attempt to solve:

Simplifying
11 + -10x + x2 = 0

Solving
11 + -10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-11' to each side of the equation.
11 + -10x + -11 + x2 = 0 + -11

Reorder the terms:
11 + -11 + -10x + x2 = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -10x + x2 = 0 + -11
-10x + x2 = 0 + -11

Combine like terms: 0 + -11 = -11
-10x + x2 = -11

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 = -11 + 25

Reorder the terms:
25 + -10x + x2 = -11 + 25

Combine like terms: -11 + 25 = 14
25 + -10x + x2 = 14

Factor a perfect square on the left side:
(x + -5)(x + -5) = 14

Calculate the square root of the right side: 3.741657387

Break this problem into two subproblems by setting 
(x + -5) equal to 3.741657387 and -3.741657387.


Subproblem 1
x + -5 = 3.741657387

Simplifying
x + -5 = 3.741657387

Reorder the terms:
-5 + x = 3.741657387

Solving
-5 + x = 3.741657387

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 = 3.741657387 + 5

Combine like terms: -5 + 5 = 0
0 + x = 3.741657387 + 5
x = 3.741657387 + 5

Combine like terms: 3.741657387 + 5 = 8.741657387
x = 8.741657387

Simplifying
x = 8.741657387


Subproblem 2
x + -5 = -3.741657387

Simplifying
x + -5 = -3.741657387

Reorder the terms:
-5 + x = -3.741657387

Solving
-5 + x = -3.741657387

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 = -3.741657387 + 5

Combine like terms: -5 + 5 = 0
0 + x = -3.741657387 + 5
x = -3.741657387 + 5

Combine like terms: -3.741657387 + 5 = 1.258342613
x = 1.258342613

Simplifying
x = 1.258342613


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.741657387, 1.258342613}
Solution
x = {8.741657387, 1.258342613}

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