2x(2-x)=x(2-x)+35

Solution for 2x(2-x)=x(2-x)+35 equation:

Simplifying
2x(2 + -1x) = x(2 + -1x) + 35
(2 * 2x + -1x * 2x) = x(2 + -1x) + 35
(4x + -2x2) = x(2 + -1x) + 35
4x + -2x2 = (2 * x + -1x * x) + 35
4x + -2x2 = (2x + -1x2) + 35

Reorder the terms:
4x + -2x2 = 35 + 2x + -1x2

Solving
4x + -2x2 = 35 + 2x + -1x2

Solving for variable 'x'.

Reorder the terms:
-35 + 4x + -2x + -2x2 + x2 = 35 + 2x + -1x2 + -35 + -2x + x2

Combine like terms: 4x + -2x = 2x
-35 + 2x + -2x2 + x2 = 35 + 2x + -1x2 + -35 + -2x + x2

Combine like terms: -2x2 + x2 = -1x2
-35 + 2x + -1x2 = 35 + 2x + -1x2 + -35 + -2x + x2

Reorder the terms:
-35 + 2x + -1x2 = 35 + -35 + 2x + -2x + -1x2 + x2

Combine like terms: 35 + -35 = 0
-35 + 2x + -1x2 = 0 + 2x + -2x + -1x2 + x2
-35 + 2x + -1x2 = 2x + -2x + -1x2 + x2

Combine like terms: 2x + -2x = 0
-35 + 2x + -1x2 = 0 + -1x2 + x2
-35 + 2x + -1x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-35 + 2x + -1x2 = 0

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

Divide each side by '-1'.
35 + -2x + x2 = 0

Move the constant term to the right:

Add '-35' to each side of the equation.
35 + -2x + -35 + x2 = 0 + -35

Reorder the terms:
35 + -35 + -2x + x2 = 0 + -35

Combine like terms: 35 + -35 = 0
0 + -2x + x2 = 0 + -35
-2x + x2 = 0 + -35

Combine like terms: 0 + -35 = -35
-2x + x2 = -35

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 = -35 + 1

Reorder the terms:
1 + -2x + x2 = -35 + 1

Combine like terms: -35 + 1 = -34
1 + -2x + x2 = -34

Factor a perfect square on the left side:
(x + -1)(x + -1) = -34

Can't calculate square root of the right side.

The solution to this equation could not be determined.