-3=a^2-3a+6

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Solution for -3=a^2-3a+6 equation:


Simplifying
-3 = a2 + -3a + 6

Reorder the terms:
-3 = 6 + -3a + a2

Solving
-3 = 6 + -3a + a2

Solving for variable 'a'.

Combine like terms: -3 + -6 = -9
-9 + 3a + -1a2 = 6 + -3a + a2 + -6 + 3a + -1a2

Reorder the terms:
-9 + 3a + -1a2 = 6 + -6 + -3a + 3a + a2 + -1a2

Combine like terms: 6 + -6 = 0
-9 + 3a + -1a2 = 0 + -3a + 3a + a2 + -1a2
-9 + 3a + -1a2 = -3a + 3a + a2 + -1a2

Combine like terms: -3a + 3a = 0
-9 + 3a + -1a2 = 0 + a2 + -1a2
-9 + 3a + -1a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
-9 + 3a + -1a2 = 0

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

Divide each side by '-1'.
9 + -3a + a2 = 0

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + -3a + -9 + a2 = 0 + -9

Reorder the terms:
9 + -9 + -3a + a2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -3a + a2 = 0 + -9
-3a + a2 = 0 + -9

Combine like terms: 0 + -9 = -9
-3a + a2 = -9

The a term is -3a.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3a + 2.25 + a2 = -9 + 2.25

Reorder the terms:
2.25 + -3a + a2 = -9 + 2.25

Combine like terms: -9 + 2.25 = -6.75
2.25 + -3a + a2 = -6.75

Factor a perfect square on the left side:
(a + -1.5)(a + -1.5) = -6.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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