a^2=3a-10

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Solution for a^2=3a-10 equation:


Simplifying
a2 = 3a + -10

Reorder the terms:
a2 = -10 + 3a

Solving
a2 = -10 + 3a

Solving for variable 'a'.

Reorder the terms:
10 + -3a + a2 = -10 + 3a + 10 + -3a

Reorder the terms:
10 + -3a + a2 = -10 + 10 + 3a + -3a

Combine like terms: -10 + 10 = 0
10 + -3a + a2 = 0 + 3a + -3a
10 + -3a + a2 = 3a + -3a

Combine like terms: 3a + -3a = 0
10 + -3a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + -3a + -10 + a2 = 0 + -10

Reorder the terms:
10 + -10 + -3a + a2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -3a + a2 = 0 + -10
-3a + a2 = 0 + -10

Combine like terms: 0 + -10 = -10
-3a + a2 = -10

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 = -10 + 2.25

Reorder the terms:
2.25 + -3a + a2 = -10 + 2.25

Combine like terms: -10 + 2.25 = -7.75
2.25 + -3a + a2 = -7.75

Factor a perfect square on the left side:
(a + -1.5)(a + -1.5) = -7.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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