3a^2-12a=16

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Solution for 3a^2-12a=16 equation:


Simplifying
3a2 + -12a = 16

Reorder the terms:
-12a + 3a2 = 16

Solving
-12a + 3a2 = 16

Solving for variable 'a'.

Reorder the terms:
-16 + -12a + 3a2 = 16 + -16

Combine like terms: 16 + -16 = 0
-16 + -12a + 3a2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
-5.333333333 + -4a + a2 = 0

Move the constant term to the right:

Add '5.333333333' to each side of the equation.
-5.333333333 + -4a + 5.333333333 + a2 = 0 + 5.333333333

Reorder the terms:
-5.333333333 + 5.333333333 + -4a + a2 = 0 + 5.333333333

Combine like terms: -5.333333333 + 5.333333333 = 0.000000000
0.000000000 + -4a + a2 = 0 + 5.333333333
-4a + a2 = 0 + 5.333333333

Combine like terms: 0 + 5.333333333 = 5.333333333
-4a + a2 = 5.333333333

The a term is -4a.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4a + 4 + a2 = 5.333333333 + 4

Reorder the terms:
4 + -4a + a2 = 5.333333333 + 4

Combine like terms: 5.333333333 + 4 = 9.333333333
4 + -4a + a2 = 9.333333333

Factor a perfect square on the left side:
(a + -2)(a + -2) = 9.333333333

Calculate the square root of the right side: 3.055050463

Break this problem into two subproblems by setting 
(a + -2) equal to 3.055050463 and -3.055050463.

Subproblem 1

a + -2 = 3.055050463 Simplifying a + -2 = 3.055050463 Reorder the terms: -2 + a = 3.055050463 Solving -2 + a = 3.055050463 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + a = 3.055050463 + 2 Combine like terms: -2 + 2 = 0 0 + a = 3.055050463 + 2 a = 3.055050463 + 2 Combine like terms: 3.055050463 + 2 = 5.055050463 a = 5.055050463 Simplifying a = 5.055050463

Subproblem 2

a + -2 = -3.055050463 Simplifying a + -2 = -3.055050463 Reorder the terms: -2 + a = -3.055050463 Solving -2 + a = -3.055050463 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + a = -3.055050463 + 2 Combine like terms: -2 + 2 = 0 0 + a = -3.055050463 + 2 a = -3.055050463 + 2 Combine like terms: -3.055050463 + 2 = -1.055050463 a = -1.055050463 Simplifying a = -1.055050463

Solution

The solution to the problem is based on the solutions from the subproblems. a = {5.055050463, -1.055050463}

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