a^2=2a-3

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


Simplifying
a2 = 2a + -3

Reorder the terms:
a2 = -3 + 2a

Solving
a2 = -3 + 2a

Solving for variable 'a'.

Reorder the terms:
3 + -2a + a2 = -3 + 2a + 3 + -2a

Reorder the terms:
3 + -2a + a2 = -3 + 3 + 2a + -2a

Combine like terms: -3 + 3 = 0
3 + -2a + a2 = 0 + 2a + -2a
3 + -2a + a2 = 2a + -2a

Combine like terms: 2a + -2a = 0
3 + -2a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -2a + -3 + a2 = 0 + -3

Reorder the terms:
3 + -3 + -2a + a2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2a + a2 = 0 + -3
-2a + a2 = 0 + -3

Combine like terms: 0 + -3 = -3
-2a + a2 = -3

The a term is -2a.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2a + 1 + a2 = -3 + 1

Reorder the terms:
1 + -2a + a2 = -3 + 1

Combine like terms: -3 + 1 = -2
1 + -2a + a2 = -2

Factor a perfect square on the left side:
(a + -1)(a + -1) = -2

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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