2a^2+3a=16

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Solution for 2a^2+3a=16 equation:


Simplifying
2a2 + 3a = 16

Reorder the terms:
3a + 2a2 = 16

Solving
3a + 2a2 = 16

Solving for variable 'a'.

Reorder the terms:
-16 + 3a + 2a2 = 16 + -16

Combine like terms: 16 + -16 = 0
-16 + 3a + 2a2 = 0

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

Divide each side by '2'.
-8 + 1.5a + a2 = 0

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + 1.5a + 8 + a2 = 0 + 8

Reorder the terms:
-8 + 8 + 1.5a + a2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 1.5a + a2 = 0 + 8
1.5a + a2 = 0 + 8

Combine like terms: 0 + 8 = 8
1.5a + a2 = 8

The a term is 1.5a.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5a + 0.5625 + a2 = 8 + 0.5625

Reorder the terms:
0.5625 + 1.5a + a2 = 8 + 0.5625

Combine like terms: 8 + 0.5625 = 8.5625
0.5625 + 1.5a + a2 = 8.5625

Factor a perfect square on the left side:
(a + 0.75)(a + 0.75) = 8.5625

Calculate the square root of the right side: 2.926174978

Break this problem into two subproblems by setting 
(a + 0.75) equal to 2.926174978 and -2.926174978.

Subproblem 1

a + 0.75 = 2.926174978 Simplifying a + 0.75 = 2.926174978 Reorder the terms: 0.75 + a = 2.926174978 Solving 0.75 + a = 2.926174978 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + a = 2.926174978 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + a = 2.926174978 + -0.75 a = 2.926174978 + -0.75 Combine like terms: 2.926174978 + -0.75 = 2.176174978 a = 2.176174978 Simplifying a = 2.176174978

Subproblem 2

a + 0.75 = -2.926174978 Simplifying a + 0.75 = -2.926174978 Reorder the terms: 0.75 + a = -2.926174978 Solving 0.75 + a = -2.926174978 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + a = -2.926174978 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + a = -2.926174978 + -0.75 a = -2.926174978 + -0.75 Combine like terms: -2.926174978 + -0.75 = -3.676174978 a = -3.676174978 Simplifying a = -3.676174978

Solution

The solution to the problem is based on the solutions from the subproblems. a = {2.176174978, -3.676174978}

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