3a^2+8a-72=0

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Solution for 3a^2+8a-72=0 equation:


Simplifying
3a2 + 8a + -72 = 0

Reorder the terms:
-72 + 8a + 3a2 = 0

Solving
-72 + 8a + 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'.
-24 + 2.666666667a + a2 = 0

Move the constant term to the right:

Add '24' to each side of the equation.
-24 + 2.666666667a + 24 + a2 = 0 + 24

Reorder the terms:
-24 + 24 + 2.666666667a + a2 = 0 + 24

Combine like terms: -24 + 24 = 0
0 + 2.666666667a + a2 = 0 + 24
2.666666667a + a2 = 0 + 24

Combine like terms: 0 + 24 = 24
2.666666667a + a2 = 24

The a term is 2.666666667a.  Take half its coefficient (1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
2.666666667a + 1.777777780 + a2 = 24 + 1.777777780

Reorder the terms:
1.777777780 + 2.666666667a + a2 = 24 + 1.777777780

Combine like terms: 24 + 1.777777780 = 25.77777778
1.777777780 + 2.666666667a + a2 = 25.77777778

Factor a perfect square on the left side:
(a + 1.333333334)(a + 1.333333334) = 25.77777778

Calculate the square root of the right side: 5.077182071

Break this problem into two subproblems by setting 
(a + 1.333333334) equal to 5.077182071 and -5.077182071.

Subproblem 1

a + 1.333333334 = 5.077182071 Simplifying a + 1.333333334 = 5.077182071 Reorder the terms: 1.333333334 + a = 5.077182071 Solving 1.333333334 + a = 5.077182071 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + a = 5.077182071 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + a = 5.077182071 + -1.333333334 a = 5.077182071 + -1.333333334 Combine like terms: 5.077182071 + -1.333333334 = 3.743848737 a = 3.743848737 Simplifying a = 3.743848737

Subproblem 2

a + 1.333333334 = -5.077182071 Simplifying a + 1.333333334 = -5.077182071 Reorder the terms: 1.333333334 + a = -5.077182071 Solving 1.333333334 + a = -5.077182071 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + a = -5.077182071 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + a = -5.077182071 + -1.333333334 a = -5.077182071 + -1.333333334 Combine like terms: -5.077182071 + -1.333333334 = -6.410515405 a = -6.410515405 Simplifying a = -6.410515405

Solution

The solution to the problem is based on the solutions from the subproblems. a = {3.743848737, -6.410515405}

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