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Simplifying a2 + -8a + -24 = 0 Reorder the terms: -24 + -8a + a2 = 0 Solving -24 + -8a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '24' to each side of the equation. -24 + -8a + 24 + a2 = 0 + 24 Reorder the terms: -24 + 24 + -8a + a2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -8a + a2 = 0 + 24 -8a + a2 = 0 + 24 Combine like terms: 0 + 24 = 24 -8a + a2 = 24 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 = 24 + 16 Reorder the terms: 16 + -8a + a2 = 24 + 16 Combine like terms: 24 + 16 = 40 16 + -8a + a2 = 40 Factor a perfect square on the left side: (a + -4)(a + -4) = 40 Calculate the square root of the right side: 6.32455532 Break this problem into two subproblems by setting (a + -4) equal to 6.32455532 and -6.32455532.Subproblem 1
a + -4 = 6.32455532 Simplifying a + -4 = 6.32455532 Reorder the terms: -4 + a = 6.32455532 Solving -4 + a = 6.32455532 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 = 6.32455532 + 4 Combine like terms: -4 + 4 = 0 0 + a = 6.32455532 + 4 a = 6.32455532 + 4 Combine like terms: 6.32455532 + 4 = 10.32455532 a = 10.32455532 Simplifying a = 10.32455532Subproblem 2
a + -4 = -6.32455532 Simplifying a + -4 = -6.32455532 Reorder the terms: -4 + a = -6.32455532 Solving -4 + a = -6.32455532 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 = -6.32455532 + 4 Combine like terms: -4 + 4 = 0 0 + a = -6.32455532 + 4 a = -6.32455532 + 4 Combine like terms: -6.32455532 + 4 = -2.32455532 a = -2.32455532 Simplifying a = -2.32455532Solution
The solution to the problem is based on the solutions from the subproblems. a = {10.32455532, -2.32455532}
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