3a^2+24a-169=0

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Solution for 3a^2+24a-169=0 equation:


Simplifying
3a2 + 24a + -169 = 0

Reorder the terms:
-169 + 24a + 3a2 = 0

Solving
-169 + 24a + 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'.
-56.33333333 + 8a + a2 = 0

Move the constant term to the right:

Add '56.33333333' to each side of the equation.
-56.33333333 + 8a + 56.33333333 + a2 = 0 + 56.33333333

Reorder the terms:
-56.33333333 + 56.33333333 + 8a + a2 = 0 + 56.33333333

Combine like terms: -56.33333333 + 56.33333333 = 0.00000000
0.00000000 + 8a + a2 = 0 + 56.33333333
8a + a2 = 0 + 56.33333333

Combine like terms: 0 + 56.33333333 = 56.33333333
8a + a2 = 56.33333333

The a term is 8a.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8a + 16 + a2 = 56.33333333 + 16

Reorder the terms:
16 + 8a + a2 = 56.33333333 + 16

Combine like terms: 56.33333333 + 16 = 72.33333333
16 + 8a + a2 = 72.33333333

Factor a perfect square on the left side:
(a + 4)(a + 4) = 72.33333333

Calculate the square root of the right side: 8.504900548

Break this problem into two subproblems by setting 
(a + 4) equal to 8.504900548 and -8.504900548.

Subproblem 1

a + 4 = 8.504900548 Simplifying a + 4 = 8.504900548 Reorder the terms: 4 + a = 8.504900548 Solving 4 + a = 8.504900548 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + a = 8.504900548 + -4 Combine like terms: 4 + -4 = 0 0 + a = 8.504900548 + -4 a = 8.504900548 + -4 Combine like terms: 8.504900548 + -4 = 4.504900548 a = 4.504900548 Simplifying a = 4.504900548

Subproblem 2

a + 4 = -8.504900548 Simplifying a + 4 = -8.504900548 Reorder the terms: 4 + a = -8.504900548 Solving 4 + a = -8.504900548 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + a = -8.504900548 + -4 Combine like terms: 4 + -4 = 0 0 + a = -8.504900548 + -4 a = -8.504900548 + -4 Combine like terms: -8.504900548 + -4 = -12.504900548 a = -12.504900548 Simplifying a = -12.504900548

Solution

The solution to the problem is based on the solutions from the subproblems. a = {4.504900548, -12.504900548}

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