64=2a+a^2+1

Solution for 64=2a+a^2+1 equation:

Simplifying
64 = 2a + a2 + 1

Reorder the terms:
64 = 1 + 2a + a2

Solving
64 = 1 + 2a + a2

Solving for variable 'a'.

Combine like terms: 64 + -1 = 63
63 + -2a + -1a2 = 1 + 2a + a2 + -1 + -2a + -1a2

Reorder the terms:
63 + -2a + -1a2 = 1 + -1 + 2a + -2a + a2 + -1a2

Combine like terms: 1 + -1 = 0
63 + -2a + -1a2 = 0 + 2a + -2a + a2 + -1a2
63 + -2a + -1a2 = 2a + -2a + a2 + -1a2

Combine like terms: 2a + -2a = 0
63 + -2a + -1a2 = 0 + a2 + -1a2
63 + -2a + -1a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
63 + -2a + -1a2 = 0

Factor a trinomial.
(7 + -1a)(9 + a) = 0

Subproblem 1
Set the factor '(7 + -1a)' equal to zero and attempt to solve:

Simplifying
7 + -1a = 0

Solving
7 + -1a = 0

Move all terms containing a to the left, all other terms to the right.

Add '-7' to each side of the equation.
7 + -7 + -1a = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1a = 0 + -7
-1a = 0 + -7

Combine like terms: 0 + -7 = -7
-1a = -7

Divide each side by '-1'.
a = 7

Simplifying
a = 7
Subproblem 2
Set the factor '(9 + a)' equal to zero and attempt to solve:

Simplifying
9 + a = 0

Solving
9 + a = 0

Move all terms containing a to the left, all other terms to the right.

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

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

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

Simplifying
a = -9
Solution
a = {7, -9}