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Simplifying 4a2 + -1a + -24 = 0 Reorder the terms: -24 + -1a + 4a2 = 0 Solving -24 + -1a + 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 + -0.25a + a2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -0.25a + 6 + a2 = 0 + 6 Reorder the terms: -6 + 6 + -0.25a + a2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -0.25a + a2 = 0 + 6 -0.25a + a2 = 0 + 6 Combine like terms: 0 + 6 = 6 -0.25a + a2 = 6 The a term is -0.25a. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25a + 0.015625 + a2 = 6 + 0.015625 Reorder the terms: 0.015625 + -0.25a + a2 = 6 + 0.015625 Combine like terms: 6 + 0.015625 = 6.015625 0.015625 + -0.25a + a2 = 6.015625 Factor a perfect square on the left side: (a + -0.125)(a + -0.125) = 6.015625 Calculate the square root of the right side: 2.452677109 Break this problem into two subproblems by setting (a + -0.125) equal to 2.452677109 and -2.452677109.Subproblem 1
a + -0.125 = 2.452677109 Simplifying a + -0.125 = 2.452677109 Reorder the terms: -0.125 + a = 2.452677109 Solving -0.125 + a = 2.452677109 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + a = 2.452677109 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + a = 2.452677109 + 0.125 a = 2.452677109 + 0.125 Combine like terms: 2.452677109 + 0.125 = 2.577677109 a = 2.577677109 Simplifying a = 2.577677109Subproblem 2
a + -0.125 = -2.452677109 Simplifying a + -0.125 = -2.452677109 Reorder the terms: -0.125 + a = -2.452677109 Solving -0.125 + a = -2.452677109 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + a = -2.452677109 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + a = -2.452677109 + 0.125 a = -2.452677109 + 0.125 Combine like terms: -2.452677109 + 0.125 = -2.327677109 a = -2.327677109 Simplifying a = -2.327677109Solution
The solution to the problem is based on the solutions from the subproblems. a = {2.577677109, -2.327677109}
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