3a^2+13a-39=

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Solution for 3a^2+13a-39= equation:


Simplifying
3a2 + 13a + -39 = 0

Reorder the terms:
-39 + 13a + 3a2 = 0

Solving
-39 + 13a + 3a2 = 0

Solving for variable 'a'.

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

Divide each side by '3'.
-13 + 4.333333333a + a2 = 0

Move the constant term to the right:

Add '13' to each side of the equation.
-13 + 4.333333333a + 13 + a2 = 0 + 13

Reorder the terms:
-13 + 13 + 4.333333333a + a2 = 0 + 13

Combine like terms: -13 + 13 = 0
0 + 4.333333333a + a2 = 0 + 13
4.333333333a + a2 = 0 + 13

Combine like terms: 0 + 13 = 13
4.333333333a + a2 = 13

The a term is 4.333333333a.  Take half its coefficient (2.166666667).
Square it (4.694444446) and add it to both sides.

Add '4.694444446' to each side of the equation.
4.333333333a + 4.694444446 + a2 = 13 + 4.694444446

Reorder the terms:
4.694444446 + 4.333333333a + a2 = 13 + 4.694444446

Combine like terms: 13 + 4.694444446 = 17.694444446
4.694444446 + 4.333333333a + a2 = 17.694444446

Factor a perfect square on the left side:
(a + 2.166666667)(a + 2.166666667) = 17.694444446

Calculate the square root of the right side: 4.206476488

Break this problem into two subproblems by setting 
(a + 2.166666667) equal to 4.206476488 and -4.206476488.

Subproblem 1

a + 2.166666667 = 4.206476488 Simplifying a + 2.166666667 = 4.206476488 Reorder the terms: 2.166666667 + a = 4.206476488 Solving 2.166666667 + a = 4.206476488 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2.166666667' to each side of the equation. 2.166666667 + -2.166666667 + a = 4.206476488 + -2.166666667 Combine like terms: 2.166666667 + -2.166666667 = 0.000000000 0.000000000 + a = 4.206476488 + -2.166666667 a = 4.206476488 + -2.166666667 Combine like terms: 4.206476488 + -2.166666667 = 2.039809821 a = 2.039809821 Simplifying a = 2.039809821

Subproblem 2

a + 2.166666667 = -4.206476488 Simplifying a + 2.166666667 = -4.206476488 Reorder the terms: 2.166666667 + a = -4.206476488 Solving 2.166666667 + a = -4.206476488 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2.166666667' to each side of the equation. 2.166666667 + -2.166666667 + a = -4.206476488 + -2.166666667 Combine like terms: 2.166666667 + -2.166666667 = 0.000000000 0.000000000 + a = -4.206476488 + -2.166666667 a = -4.206476488 + -2.166666667 Combine like terms: -4.206476488 + -2.166666667 = -6.373143155 a = -6.373143155 Simplifying a = -6.373143155

Solution

The solution to the problem is based on the solutions from the subproblems. a = {2.039809821, -6.373143155}

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