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Simplifying 2a2 + 15a + -250 = 0 Reorder the terms: -250 + 15a + 2a2 = 0 Solving -250 + 15a + 2a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -125 + 7.5a + a2 = 0 Move the constant term to the right: Add '125' to each side of the equation. -125 + 7.5a + 125 + a2 = 0 + 125 Reorder the terms: -125 + 125 + 7.5a + a2 = 0 + 125 Combine like terms: -125 + 125 = 0 0 + 7.5a + a2 = 0 + 125 7.5a + a2 = 0 + 125 Combine like terms: 0 + 125 = 125 7.5a + a2 = 125 The a term is 7.5a. Take half its coefficient (3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. 7.5a + 14.0625 + a2 = 125 + 14.0625 Reorder the terms: 14.0625 + 7.5a + a2 = 125 + 14.0625 Combine like terms: 125 + 14.0625 = 139.0625 14.0625 + 7.5a + a2 = 139.0625 Factor a perfect square on the left side: (a + 3.75)(a + 3.75) = 139.0625 Calculate the square root of the right side: 11.792476415 Break this problem into two subproblems by setting (a + 3.75) equal to 11.792476415 and -11.792476415.Subproblem 1
a + 3.75 = 11.792476415 Simplifying a + 3.75 = 11.792476415 Reorder the terms: 3.75 + a = 11.792476415 Solving 3.75 + a = 11.792476415 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + a = 11.792476415 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + a = 11.792476415 + -3.75 a = 11.792476415 + -3.75 Combine like terms: 11.792476415 + -3.75 = 8.042476415 a = 8.042476415 Simplifying a = 8.042476415Subproblem 2
a + 3.75 = -11.792476415 Simplifying a + 3.75 = -11.792476415 Reorder the terms: 3.75 + a = -11.792476415 Solving 3.75 + a = -11.792476415 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + a = -11.792476415 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + a = -11.792476415 + -3.75 a = -11.792476415 + -3.75 Combine like terms: -11.792476415 + -3.75 = -15.542476415 a = -15.542476415 Simplifying a = -15.542476415Solution
The solution to the problem is based on the solutions from the subproblems. a = {8.042476415, -15.542476415}
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