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Simplifying 4a2 + 24a + 9 = 0 Reorder the terms: 9 + 24a + 4a2 = 0 Solving 9 + 24a + 4a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2.25 + 6a + a2 = 0 Move the constant term to the right: Add '-2.25' to each side of the equation. 2.25 + 6a + -2.25 + a2 = 0 + -2.25 Reorder the terms: 2.25 + -2.25 + 6a + a2 = 0 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + 6a + a2 = 0 + -2.25 6a + a2 = 0 + -2.25 Combine like terms: 0 + -2.25 = -2.25 6a + a2 = -2.25 The a term is 6a. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6a + 9 + a2 = -2.25 + 9 Reorder the terms: 9 + 6a + a2 = -2.25 + 9 Combine like terms: -2.25 + 9 = 6.75 9 + 6a + a2 = 6.75 Factor a perfect square on the left side: (a + 3)(a + 3) = 6.75 Calculate the square root of the right side: 2.598076211 Break this problem into two subproblems by setting (a + 3) equal to 2.598076211 and -2.598076211.Subproblem 1
a + 3 = 2.598076211 Simplifying a + 3 = 2.598076211 Reorder the terms: 3 + a = 2.598076211 Solving 3 + a = 2.598076211 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + a = 2.598076211 + -3 Combine like terms: 3 + -3 = 0 0 + a = 2.598076211 + -3 a = 2.598076211 + -3 Combine like terms: 2.598076211 + -3 = -0.401923789 a = -0.401923789 Simplifying a = -0.401923789Subproblem 2
a + 3 = -2.598076211 Simplifying a + 3 = -2.598076211 Reorder the terms: 3 + a = -2.598076211 Solving 3 + a = -2.598076211 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + a = -2.598076211 + -3 Combine like terms: 3 + -3 = 0 0 + a = -2.598076211 + -3 a = -2.598076211 + -3 Combine like terms: -2.598076211 + -3 = -5.598076211 a = -5.598076211 Simplifying a = -5.598076211Solution
The solution to the problem is based on the solutions from the subproblems. a = {-0.401923789, -5.598076211}
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