18-2x=20+x^2

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Solution for 18-2x=20+x^2 equation: 


Simplifying
18 + -2x = 20 + x2

Solving
18 + -2x = 20 + x2

Solving for variable 'x'.

Reorder the terms:
18 + -20 + -2x + -1x2 = 20 + x2 + -20 + -1x2

Combine like terms: 18 + -20 = -2
-2 + -2x + -1x2 = 20 + x2 + -20 + -1x2

Reorder the terms:
-2 + -2x + -1x2 = 20 + -20 + x2 + -1x2

Combine like terms: 20 + -20 = 0
-2 + -2x + -1x2 = 0 + x2 + -1x2
-2 + -2x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-2 + -2x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(2 + 2x + x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(2 + 2x + x2)' equal to zero and attempt to solve:

Simplifying
2 + 2x + x2 = 0

Solving
2 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 2x + -2 + x2 = 0 + -2

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

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

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

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = -2 + 1

Reorder the terms:
1 + 2x + x2 = -2 + 1

Combine like terms: -2 + 1 = -1
1 + 2x + x2 = -1

Factor a perfect square on the left side:
(x + 1)(x + 1) = -1

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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