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Simplifying 24a2 + a + -15 = 0 Reorder the terms: -15 + a + 24a2 = 0 Solving -15 + a + 24a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. -0.625 + 0.04166666667a + a2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + 0.04166666667a + 0.625 + a2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + 0.04166666667a + a2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + 0.04166666667a + a2 = 0 + 0.625 0.04166666667a + a2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 0.04166666667a + a2 = 0.625 The a term is a. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.04166666667a + 0.25 + a2 = 0.625 + 0.25 Reorder the terms: 0.25 + 0.04166666667a + a2 = 0.625 + 0.25 Combine like terms: 0.625 + 0.25 = 0.875 0.25 + 0.04166666667a + a2 = 0.875 Factor a perfect square on the left side: (a + 0.5)(a + 0.5) = 0.875 Calculate the square root of the right side: 0.935414347 Break this problem into two subproblems by setting (a + 0.5) equal to 0.935414347 and -0.935414347.Subproblem 1
a + 0.5 = 0.935414347 Simplifying a + 0.5 = 0.935414347 Reorder the terms: 0.5 + a = 0.935414347 Solving 0.5 + a = 0.935414347 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + a = 0.935414347 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = 0.935414347 + -0.5 a = 0.935414347 + -0.5 Combine like terms: 0.935414347 + -0.5 = 0.435414347 a = 0.435414347 Simplifying a = 0.435414347Subproblem 2
a + 0.5 = -0.935414347 Simplifying a + 0.5 = -0.935414347 Reorder the terms: 0.5 + a = -0.935414347 Solving 0.5 + a = -0.935414347 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + a = -0.935414347 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = -0.935414347 + -0.5 a = -0.935414347 + -0.5 Combine like terms: -0.935414347 + -0.5 = -1.435414347 a = -1.435414347 Simplifying a = -1.435414347Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.435414347, -1.435414347}
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