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Simplifying 2a2 + 2a + -15 = 0 Reorder the terms: -15 + 2a + 2a2 = 0 Solving -15 + 2a + 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'. -7.5 + a + a2 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + a + 7.5 + a2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + a + a2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + a + a2 = 0 + 7.5 a + a2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 a + a2 = 7.5 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. + 0.25 + a2 = 7.5 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + a2 = 7.5 + 0.25 Combine like terms: 7.5 + 0.25 = 7.75 1.25 + a2 = 7.75 Factor a perfect square on the left side: (a + 0.5)(a + 0.5) = 7.75 Calculate the square root of the right side: 2.783882181 Break this problem into two subproblems by setting (a + 0.5) equal to 2.783882181 and -2.783882181.Subproblem 1
a + 0.5 = 2.783882181 Simplifying a + 0.5 = 2.783882181 Reorder the terms: 0.5 + a = 2.783882181 Solving 0.5 + a = 2.783882181 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 = 2.783882181 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = 2.783882181 + -0.5 a = 2.783882181 + -0.5 Combine like terms: 2.783882181 + -0.5 = 2.283882181 a = 2.283882181 Simplifying a = 2.283882181Subproblem 2
a + 0.5 = -2.783882181 Simplifying a + 0.5 = -2.783882181 Reorder the terms: 0.5 + a = -2.783882181 Solving 0.5 + a = -2.783882181 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 = -2.783882181 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = -2.783882181 + -0.5 a = -2.783882181 + -0.5 Combine like terms: -2.783882181 + -0.5 = -3.283882181 a = -3.283882181 Simplifying a = -3.283882181Solution
The solution to the problem is based on the solutions from the subproblems. a = {2.283882181, -3.283882181}
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