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Simplifying a2 + 3a + -24 = 0 Reorder the terms: -24 + 3a + a2 = 0 Solving -24 + 3a + 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 + 3a + 24 + a2 = 0 + 24 Reorder the terms: -24 + 24 + 3a + a2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + 3a + a2 = 0 + 24 3a + a2 = 0 + 24 Combine like terms: 0 + 24 = 24 3a + a2 = 24 The a term is 3a. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3a + 2.25 + a2 = 24 + 2.25 Reorder the terms: 2.25 + 3a + a2 = 24 + 2.25 Combine like terms: 24 + 2.25 = 26.25 2.25 + 3a + a2 = 26.25 Factor a perfect square on the left side: (a + 1.5)(a + 1.5) = 26.25 Calculate the square root of the right side: 5.123475383 Break this problem into two subproblems by setting (a + 1.5) equal to 5.123475383 and -5.123475383.Subproblem 1
a + 1.5 = 5.123475383 Simplifying a + 1.5 = 5.123475383 Reorder the terms: 1.5 + a = 5.123475383 Solving 1.5 + a = 5.123475383 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + a = 5.123475383 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + a = 5.123475383 + -1.5 a = 5.123475383 + -1.5 Combine like terms: 5.123475383 + -1.5 = 3.623475383 a = 3.623475383 Simplifying a = 3.623475383Subproblem 2
a + 1.5 = -5.123475383 Simplifying a + 1.5 = -5.123475383 Reorder the terms: 1.5 + a = -5.123475383 Solving 1.5 + a = -5.123475383 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + a = -5.123475383 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + a = -5.123475383 + -1.5 a = -5.123475383 + -1.5 Combine like terms: -5.123475383 + -1.5 = -6.623475383 a = -6.623475383 Simplifying a = -6.623475383Solution
The solution to the problem is based on the solutions from the subproblems. a = {3.623475383, -6.623475383}
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