2x-2x^2=42

Solution for 2x-2x^2=42 equation:

Simplifying
2x + -2x2 = 42

Solving
2x + -2x2 = 42

Solving for variable 'x'.

Reorder the terms:
-42 + 2x + -2x2 = 42 + -42

Combine like terms: 42 + -42 = 0
-42 + 2x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-21 + x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-21 + x + -1x2)' equal to zero and attempt to solve:

Simplifying
-21 + x + -1x2 = 0

Solving
-21 + x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
21 + -1x + x2 = 0

Move the constant term to the right:

Add '-21' to each side of the equation.
21 + -1x + -21 + x2 = 0 + -21

Reorder the terms:
21 + -21 + -1x + x2 = 0 + -21

Combine like terms: 21 + -21 = 0
0 + -1x + x2 = 0 + -21
-1x + x2 = 0 + -21

Combine like terms: 0 + -21 = -21
-1x + x2 = -21

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = -21 + 0.25

Reorder the terms:
0.25 + -1x + x2 = -21 + 0.25

Combine like terms: -21 + 0.25 = -20.75
0.25 + -1x + x2 = -20.75

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -20.75

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.