a^2+24a+72=0

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Solution for a^2+24a+72=0 equation:


Simplifying
a2 + 24a + 72 = 0

Reorder the terms:
72 + 24a + a2 = 0

Solving
72 + 24a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '-72' to each side of the equation.
72 + 24a + -72 + a2 = 0 + -72

Reorder the terms:
72 + -72 + 24a + a2 = 0 + -72

Combine like terms: 72 + -72 = 0
0 + 24a + a2 = 0 + -72
24a + a2 = 0 + -72

Combine like terms: 0 + -72 = -72
24a + a2 = -72

The a term is 24a.  Take half its coefficient (12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
24a + 144 + a2 = -72 + 144

Reorder the terms:
144 + 24a + a2 = -72 + 144

Combine like terms: -72 + 144 = 72
144 + 24a + a2 = 72

Factor a perfect square on the left side:
(a + 12)(a + 12) = 72

Calculate the square root of the right side: 8.485281374

Break this problem into two subproblems by setting 
(a + 12) equal to 8.485281374 and -8.485281374.

Subproblem 1

a + 12 = 8.485281374 Simplifying a + 12 = 8.485281374 Reorder the terms: 12 + a = 8.485281374 Solving 12 + a = 8.485281374 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + a = 8.485281374 + -12 Combine like terms: 12 + -12 = 0 0 + a = 8.485281374 + -12 a = 8.485281374 + -12 Combine like terms: 8.485281374 + -12 = -3.514718626 a = -3.514718626 Simplifying a = -3.514718626

Subproblem 2

a + 12 = -8.485281374 Simplifying a + 12 = -8.485281374 Reorder the terms: 12 + a = -8.485281374 Solving 12 + a = -8.485281374 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + a = -8.485281374 + -12 Combine like terms: 12 + -12 = 0 0 + a = -8.485281374 + -12 a = -8.485281374 + -12 Combine like terms: -8.485281374 + -12 = -20.485281374 a = -20.485281374 Simplifying a = -20.485281374

Solution

The solution to the problem is based on the solutions from the subproblems. a = {-3.514718626, -20.485281374}

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