a^2=-12a+66

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Solution for a^2=-12a+66 equation:


Simplifying
a2 = -12a + 66

Reorder the terms:
a2 = 66 + -12a

Solving
a2 = 66 + -12a

Solving for variable 'a'.

Reorder the terms:
-66 + 12a + a2 = 66 + -12a + -66 + 12a

Reorder the terms:
-66 + 12a + a2 = 66 + -66 + -12a + 12a

Combine like terms: 66 + -66 = 0
-66 + 12a + a2 = 0 + -12a + 12a
-66 + 12a + a2 = -12a + 12a

Combine like terms: -12a + 12a = 0
-66 + 12a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '66' to each side of the equation.
-66 + 12a + 66 + a2 = 0 + 66

Reorder the terms:
-66 + 66 + 12a + a2 = 0 + 66

Combine like terms: -66 + 66 = 0
0 + 12a + a2 = 0 + 66
12a + a2 = 0 + 66

Combine like terms: 0 + 66 = 66
12a + a2 = 66

The a term is 12a.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12a + 36 + a2 = 66 + 36

Reorder the terms:
36 + 12a + a2 = 66 + 36

Combine like terms: 66 + 36 = 102
36 + 12a + a2 = 102

Factor a perfect square on the left side:
(a + 6)(a + 6) = 102

Calculate the square root of the right side: 10.099504938

Break this problem into two subproblems by setting 
(a + 6) equal to 10.099504938 and -10.099504938.

Subproblem 1

a + 6 = 10.099504938 Simplifying a + 6 = 10.099504938 Reorder the terms: 6 + a = 10.099504938 Solving 6 + a = 10.099504938 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + a = 10.099504938 + -6 Combine like terms: 6 + -6 = 0 0 + a = 10.099504938 + -6 a = 10.099504938 + -6 Combine like terms: 10.099504938 + -6 = 4.099504938 a = 4.099504938 Simplifying a = 4.099504938

Subproblem 2

a + 6 = -10.099504938 Simplifying a + 6 = -10.099504938 Reorder the terms: 6 + a = -10.099504938 Solving 6 + a = -10.099504938 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + a = -10.099504938 + -6 Combine like terms: 6 + -6 = 0 0 + a = -10.099504938 + -6 a = -10.099504938 + -6 Combine like terms: -10.099504938 + -6 = -16.099504938 a = -16.099504938 Simplifying a = -16.099504938

Solution

The solution to the problem is based on the solutions from the subproblems. a = {4.099504938, -16.099504938}

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