a(a+3)+a(a-6)+35=a^2+7

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Solution for a(a+3)+a(a-6)+35=a^2+7 equation: 


Simplifying
a(a + 3) + a(a + -6) + 35 = a2 + 7

Reorder the terms:
a(3 + a) + a(a + -6) + 35 = a2 + 7
(3 * a + a * a) + a(a + -6) + 35 = a2 + 7
(3a + a2) + a(a + -6) + 35 = a2 + 7

Reorder the terms:
3a + a2 + a(-6 + a) + 35 = a2 + 7
3a + a2 + (-6 * a + a * a) + 35 = a2 + 7
3a + a2 + (-6a + a2) + 35 = a2 + 7

Reorder the terms:
35 + 3a + -6a + a2 + a2 = a2 + 7

Combine like terms: 3a + -6a = -3a
35 + -3a + a2 + a2 = a2 + 7

Combine like terms: a2 + a2 = 2a2
35 + -3a + 2a2 = a2 + 7

Reorder the terms:
35 + -3a + 2a2 = 7 + a2

Solving
35 + -3a + 2a2 = 7 + a2

Solving for variable 'a'.

Reorder the terms:
35 + -7 + -3a + 2a2 + -1a2 = 7 + a2 + -7 + -1a2

Combine like terms: 35 + -7 = 28
28 + -3a + 2a2 + -1a2 = 7 + a2 + -7 + -1a2

Combine like terms: 2a2 + -1a2 = 1a2
28 + -3a + 1a2 = 7 + a2 + -7 + -1a2

Reorder the terms:
28 + -3a + 1a2 = 7 + -7 + a2 + -1a2

Combine like terms: 7 + -7 = 0
28 + -3a + 1a2 = 0 + a2 + -1a2
28 + -3a + 1a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
28 + -3a + 1a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-28' to each side of the equation.
28 + -3a + -28 + a2 = 0 + -28

Reorder the terms:
28 + -28 + -3a + a2 = 0 + -28

Combine like terms: 28 + -28 = 0
0 + -3a + a2 = 0 + -28
-3a + a2 = 0 + -28

Combine like terms: 0 + -28 = -28
-3a + a2 = -28

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 = -28 + 2.25

Reorder the terms:
2.25 + -3a + a2 = -28 + 2.25

Combine like terms: -28 + 2.25 = -25.75
2.25 + -3a + a2 = -25.75

Factor a perfect square on the left side:
(a + -1.5)(a + -1.5) = -25.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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