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Simplifying 2a2 + -11a = 2 Reorder the terms: -11a + 2a2 = 2 Solving -11a + 2a2 = 2 Solving for variable 'a'. Reorder the terms: -2 + -11a + 2a2 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + -11a + 2a2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1 + -5.5a + a2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -5.5a + 1 + a2 = 0 + 1 Reorder the terms: -1 + 1 + -5.5a + a2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -5.5a + a2 = 0 + 1 -5.5a + a2 = 0 + 1 Combine like terms: 0 + 1 = 1 -5.5a + a2 = 1 The a term is -5.5a. Take half its coefficient (-2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. -5.5a + 7.5625 + a2 = 1 + 7.5625 Reorder the terms: 7.5625 + -5.5a + a2 = 1 + 7.5625 Combine like terms: 1 + 7.5625 = 8.5625 7.5625 + -5.5a + a2 = 8.5625 Factor a perfect square on the left side: (a + -2.75)(a + -2.75) = 8.5625 Calculate the square root of the right side: 2.926174978 Break this problem into two subproblems by setting (a + -2.75) equal to 2.926174978 and -2.926174978.Subproblem 1
a + -2.75 = 2.926174978 Simplifying a + -2.75 = 2.926174978 Reorder the terms: -2.75 + a = 2.926174978 Solving -2.75 + a = 2.926174978 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + a = 2.926174978 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + a = 2.926174978 + 2.75 a = 2.926174978 + 2.75 Combine like terms: 2.926174978 + 2.75 = 5.676174978 a = 5.676174978 Simplifying a = 5.676174978Subproblem 2
a + -2.75 = -2.926174978 Simplifying a + -2.75 = -2.926174978 Reorder the terms: -2.75 + a = -2.926174978 Solving -2.75 + a = -2.926174978 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + a = -2.926174978 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + a = -2.926174978 + 2.75 a = -2.926174978 + 2.75 Combine like terms: -2.926174978 + 2.75 = -0.176174978 a = -0.176174978 Simplifying a = -0.176174978Solution
The solution to the problem is based on the solutions from the subproblems. a = {5.676174978, -0.176174978}
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