6x+6-x^2=78

Solution for 6x+6-x^2=78 equation:

Simplifying
6x + 6 + -1x2 = 78

Reorder the terms:
6 + 6x + -1x2 = 78

Solving
6 + 6x + -1x2 = 78

Solving for variable 'x'.

Reorder the terms:
6 + -78 + 6x + -1x2 = 78 + -78

Combine like terms: 6 + -78 = -72
-72 + 6x + -1x2 = 78 + -78

Combine like terms: 78 + -78 = 0
-72 + 6x + -1x2 = 0

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

Divide each side by '-1'.
72 + -6x + x2 = 0

Move the constant term to the right:

Add '-72' to each side of the equation.
72 + -6x + -72 + x2 = 0 + -72

Reorder the terms:
72 + -72 + -6x + x2 = 0 + -72

Combine like terms: 72 + -72 = 0
0 + -6x + x2 = 0 + -72
-6x + x2 = 0 + -72

Combine like terms: 0 + -72 = -72
-6x + x2 = -72

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = -72 + 9

Reorder the terms:
9 + -6x + x2 = -72 + 9

Combine like terms: -72 + 9 = -63
9 + -6x + x2 = -63

Factor a perfect square on the left side:
(x + -3)(x + -3) = -63

Can't calculate square root of the right side.

The solution to this equation could not be determined.