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Simplifying 2a2 + -11a + -3 = 0 Reorder the terms: -3 + -11a + 2a2 = 0 Solving -3 + -11a + 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'. -1.5 + -5.5a + a2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -5.5a + 1.5 + a2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -5.5a + a2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -5.5a + a2 = 0 + 1.5 -5.5a + a2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -5.5a + a2 = 1.5 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 = 1.5 + 7.5625 Reorder the terms: 7.5625 + -5.5a + a2 = 1.5 + 7.5625 Combine like terms: 1.5 + 7.5625 = 9.0625 7.5625 + -5.5a + a2 = 9.0625 Factor a perfect square on the left side: (a + -2.75)(a + -2.75) = 9.0625 Calculate the square root of the right side: 3.010398645 Break this problem into two subproblems by setting (a + -2.75) equal to 3.010398645 and -3.010398645.Subproblem 1
a + -2.75 = 3.010398645 Simplifying a + -2.75 = 3.010398645 Reorder the terms: -2.75 + a = 3.010398645 Solving -2.75 + a = 3.010398645 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 = 3.010398645 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + a = 3.010398645 + 2.75 a = 3.010398645 + 2.75 Combine like terms: 3.010398645 + 2.75 = 5.760398645 a = 5.760398645 Simplifying a = 5.760398645Subproblem 2
a + -2.75 = -3.010398645 Simplifying a + -2.75 = -3.010398645 Reorder the terms: -2.75 + a = -3.010398645 Solving -2.75 + a = -3.010398645 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 = -3.010398645 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + a = -3.010398645 + 2.75 a = -3.010398645 + 2.75 Combine like terms: -3.010398645 + 2.75 = -0.260398645 a = -0.260398645 Simplifying a = -0.260398645Solution
The solution to the problem is based on the solutions from the subproblems. a = {5.760398645, -0.260398645}
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