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Simplifying 4a2 + -3a + -24 = 0 Reorder the terms: -24 + -3a + 4a2 = 0 Solving -24 + -3a + 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'. -6 + -0.75a + a2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -0.75a + 6 + a2 = 0 + 6 Reorder the terms: -6 + 6 + -0.75a + a2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -0.75a + a2 = 0 + 6 -0.75a + a2 = 0 + 6 Combine like terms: 0 + 6 = 6 -0.75a + a2 = 6 The a term is -0.75a. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75a + 0.140625 + a2 = 6 + 0.140625 Reorder the terms: 0.140625 + -0.75a + a2 = 6 + 0.140625 Combine like terms: 6 + 0.140625 = 6.140625 0.140625 + -0.75a + a2 = 6.140625 Factor a perfect square on the left side: (a + -0.375)(a + -0.375) = 6.140625 Calculate the square root of the right side: 2.47802845 Break this problem into two subproblems by setting (a + -0.375) equal to 2.47802845 and -2.47802845.Subproblem 1
a + -0.375 = 2.47802845 Simplifying a + -0.375 = 2.47802845 Reorder the terms: -0.375 + a = 2.47802845 Solving -0.375 + a = 2.47802845 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + a = 2.47802845 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + a = 2.47802845 + 0.375 a = 2.47802845 + 0.375 Combine like terms: 2.47802845 + 0.375 = 2.85302845 a = 2.85302845 Simplifying a = 2.85302845Subproblem 2
a + -0.375 = -2.47802845 Simplifying a + -0.375 = -2.47802845 Reorder the terms: -0.375 + a = -2.47802845 Solving -0.375 + a = -2.47802845 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + a = -2.47802845 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + a = -2.47802845 + 0.375 a = -2.47802845 + 0.375 Combine like terms: -2.47802845 + 0.375 = -2.10302845 a = -2.10302845 Simplifying a = -2.10302845Solution
The solution to the problem is based on the solutions from the subproblems. a = {2.85302845, -2.10302845}
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