2x-x^2=72

Solution for 2x-x^2=72 equation:

Simplifying
2x + -1x2 = 72

Solving
2x + -1x2 = 72

Solving for variable 'x'.

Reorder the terms:
-72 + 2x + -1x2 = 72 + -72

Combine like terms: 72 + -72 = 0
-72 + 2x + -1x2 = 0

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

Divide each side by '-1'.
72 + -2x + x2 = 0

Move the constant term to the right:

Add '-72' to each side of the equation.
72 + -2x + -72 + x2 = 0 + -72

Reorder the terms:
72 + -72 + -2x + x2 = 0 + -72

Combine like terms: 72 + -72 = 0
0 + -2x + x2 = 0 + -72
-2x + x2 = 0 + -72

Combine like terms: 0 + -72 = -72
-2x + x2 = -72

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 = -72 + 1

Reorder the terms:
1 + -2x + x2 = -72 + 1

Combine like terms: -72 + 1 = -71
1 + -2x + x2 = -71

Factor a perfect square on the left side:
(x + -1)(x + -1) = -71

Can't calculate square root of the right side.

The solution to this equation could not be determined.