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Simplifying 2a2 + -1a + -15 = 2 Reorder the terms: -15 + -1a + 2a2 = 2 Solving -15 + -1a + 2a2 = 2 Solving for variable 'a'. Reorder the terms: -15 + -2 + -1a + 2a2 = 2 + -2 Combine like terms: -15 + -2 = -17 -17 + -1a + 2a2 = 2 + -2 Combine like terms: 2 + -2 = 0 -17 + -1a + 2a2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -8.5 + -0.5a + a2 = 0 Move the constant term to the right: Add '8.5' to each side of the equation. -8.5 + -0.5a + 8.5 + a2 = 0 + 8.5 Reorder the terms: -8.5 + 8.5 + -0.5a + a2 = 0 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + -0.5a + a2 = 0 + 8.5 -0.5a + a2 = 0 + 8.5 Combine like terms: 0 + 8.5 = 8.5 -0.5a + a2 = 8.5 The a term is -0.5a. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5a + 0.0625 + a2 = 8.5 + 0.0625 Reorder the terms: 0.0625 + -0.5a + a2 = 8.5 + 0.0625 Combine like terms: 8.5 + 0.0625 = 8.5625 0.0625 + -0.5a + a2 = 8.5625 Factor a perfect square on the left side: (a + -0.25)(a + -0.25) = 8.5625 Calculate the square root of the right side: 2.926174978 Break this problem into two subproblems by setting (a + -0.25) equal to 2.926174978 and -2.926174978.Subproblem 1
a + -0.25 = 2.926174978 Simplifying a + -0.25 = 2.926174978 Reorder the terms: -0.25 + a = 2.926174978 Solving -0.25 + a = 2.926174978 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + a = 2.926174978 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + a = 2.926174978 + 0.25 a = 2.926174978 + 0.25 Combine like terms: 2.926174978 + 0.25 = 3.176174978 a = 3.176174978 Simplifying a = 3.176174978Subproblem 2
a + -0.25 = -2.926174978 Simplifying a + -0.25 = -2.926174978 Reorder the terms: -0.25 + a = -2.926174978 Solving -0.25 + a = -2.926174978 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + a = -2.926174978 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + a = -2.926174978 + 0.25 a = -2.926174978 + 0.25 Combine like terms: -2.926174978 + 0.25 = -2.676174978 a = -2.676174978 Simplifying a = -2.676174978Solution
The solution to the problem is based on the solutions from the subproblems. a = {3.176174978, -2.676174978}
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