-x+6=-x^2+3x-18

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Solution for -x+6=-x^2+3x-18 equation: 


Simplifying
-1x + 6 = -1x2 + 3x + -18

Reorder the terms:
6 + -1x = -1x2 + 3x + -18

Reorder the terms:
6 + -1x = -18 + 3x + -1x2

Solving
6 + -1x = -18 + 3x + -1x2

Solving for variable 'x'.

Reorder the terms:
6 + 18 + -1x + -3x + x2 = -18 + 3x + -1x2 + 18 + -3x + x2

Combine like terms: 6 + 18 = 24
24 + -1x + -3x + x2 = -18 + 3x + -1x2 + 18 + -3x + x2

Combine like terms: -1x + -3x = -4x
24 + -4x + x2 = -18 + 3x + -1x2 + 18 + -3x + x2

Reorder the terms:
24 + -4x + x2 = -18 + 18 + 3x + -3x + -1x2 + x2

Combine like terms: -18 + 18 = 0
24 + -4x + x2 = 0 + 3x + -3x + -1x2 + x2
24 + -4x + x2 = 3x + -3x + -1x2 + x2

Combine like terms: 3x + -3x = 0
24 + -4x + x2 = 0 + -1x2 + x2
24 + -4x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
24 + -4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-24' to each side of the equation.
24 + -4x + -24 + x2 = 0 + -24

Reorder the terms:
24 + -24 + -4x + x2 = 0 + -24

Combine like terms: 24 + -24 = 0
0 + -4x + x2 = 0 + -24
-4x + x2 = 0 + -24

Combine like terms: 0 + -24 = -24
-4x + x2 = -24

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = -24 + 4

Reorder the terms:
4 + -4x + x2 = -24 + 4

Combine like terms: -24 + 4 = -20
4 + -4x + x2 = -20

Factor a perfect square on the left side:
(x + -2)(x + -2) = -20

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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