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