17x-x^2=78

Solution for 17x-x^2=78 equation:

Simplifying
17x + -1x2 = 78

Solving
17x + -1x2 = 78

Solving for variable 'x'.

Reorder the terms:
-78 + 17x + -1x2 = 78 + -78

Combine like terms: 78 + -78 = 0
-78 + 17x + -1x2 = 0

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

Divide each side by '-1'.
78 + -17x + x2 = 0

Move the constant term to the right:

Add '-78' to each side of the equation.
78 + -17x + -78 + x2 = 0 + -78

Reorder the terms:
78 + -78 + -17x + x2 = 0 + -78

Combine like terms: 78 + -78 = 0
0 + -17x + x2 = 0 + -78
-17x + x2 = 0 + -78

Combine like terms: 0 + -78 = -78
-17x + x2 = -78

The x term is -17x.  Take half its coefficient (-8.5).
Square it (72.25) and add it to both sides.

Add '72.25' to each side of the equation.
-17x + 72.25 + x2 = -78 + 72.25

Reorder the terms:
72.25 + -17x + x2 = -78 + 72.25

Combine like terms: -78 + 72.25 = -5.75
72.25 + -17x + x2 = -5.75

Factor a perfect square on the left side:
(x + -8.5)(x + -8.5) = -5.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.