5a^2+16a=12

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Solution for 5a^2+16a=12 equation:


Simplifying
5a2 + 16a = 12

Reorder the terms:
16a + 5a2 = 12

Solving
16a + 5a2 = 12

Solving for variable 'a'.

Reorder the terms:
-12 + 16a + 5a2 = 12 + -12

Combine like terms: 12 + -12 = 0
-12 + 16a + 5a2 = 0

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

Divide each side by '5'.
-2.4 + 3.2a + a2 = 0

Move the constant term to the right:

Add '2.4' to each side of the equation.
-2.4 + 3.2a + 2.4 + a2 = 0 + 2.4

Reorder the terms:
-2.4 + 2.4 + 3.2a + a2 = 0 + 2.4

Combine like terms: -2.4 + 2.4 = 0.0
0.0 + 3.2a + a2 = 0 + 2.4
3.2a + a2 = 0 + 2.4

Combine like terms: 0 + 2.4 = 2.4
3.2a + a2 = 2.4

The a term is 3.2a.  Take half its coefficient (1.6).
Square it (2.56) and add it to both sides.

Add '2.56' to each side of the equation.
3.2a + 2.56 + a2 = 2.4 + 2.56

Reorder the terms:
2.56 + 3.2a + a2 = 2.4 + 2.56

Combine like terms: 2.4 + 2.56 = 4.96
2.56 + 3.2a + a2 = 4.96

Factor a perfect square on the left side:
(a + 1.6)(a + 1.6) = 4.96

Calculate the square root of the right side: 2.227105745

Break this problem into two subproblems by setting 
(a + 1.6) equal to 2.227105745 and -2.227105745.

Subproblem 1

a + 1.6 = 2.227105745 Simplifying a + 1.6 = 2.227105745 Reorder the terms: 1.6 + a = 2.227105745 Solving 1.6 + a = 2.227105745 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1.6' to each side of the equation. 1.6 + -1.6 + a = 2.227105745 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + a = 2.227105745 + -1.6 a = 2.227105745 + -1.6 Combine like terms: 2.227105745 + -1.6 = 0.627105745 a = 0.627105745 Simplifying a = 0.627105745

Subproblem 2

a + 1.6 = -2.227105745 Simplifying a + 1.6 = -2.227105745 Reorder the terms: 1.6 + a = -2.227105745 Solving 1.6 + a = -2.227105745 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1.6' to each side of the equation. 1.6 + -1.6 + a = -2.227105745 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + a = -2.227105745 + -1.6 a = -2.227105745 + -1.6 Combine like terms: -2.227105745 + -1.6 = -3.827105745 a = -3.827105745 Simplifying a = -3.827105745

Solution

The solution to the problem is based on the solutions from the subproblems. a = {0.627105745, -3.827105745}

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