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Simplifying 2a2 + 11a + -15 = 0 Reorder the terms: -15 + 11a + 2a2 = 0 Solving -15 + 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'. -7.5 + 5.5a + a2 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + 5.5a + 7.5 + a2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + 5.5a + a2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + 5.5a + a2 = 0 + 7.5 5.5a + a2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 5.5a + a2 = 7.5 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 = 7.5 + 7.5625 Reorder the terms: 7.5625 + 5.5a + a2 = 7.5 + 7.5625 Combine like terms: 7.5 + 7.5625 = 15.0625 7.5625 + 5.5a + a2 = 15.0625 Factor a perfect square on the left side: (a + 2.75)(a + 2.75) = 15.0625 Calculate the square root of the right side: 3.881043674 Break this problem into two subproblems by setting (a + 2.75) equal to 3.881043674 and -3.881043674.Subproblem 1
a + 2.75 = 3.881043674 Simplifying a + 2.75 = 3.881043674 Reorder the terms: 2.75 + a = 3.881043674 Solving 2.75 + a = 3.881043674 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 = 3.881043674 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + a = 3.881043674 + -2.75 a = 3.881043674 + -2.75 Combine like terms: 3.881043674 + -2.75 = 1.131043674 a = 1.131043674 Simplifying a = 1.131043674Subproblem 2
a + 2.75 = -3.881043674 Simplifying a + 2.75 = -3.881043674 Reorder the terms: 2.75 + a = -3.881043674 Solving 2.75 + a = -3.881043674 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 = -3.881043674 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + a = -3.881043674 + -2.75 a = -3.881043674 + -2.75 Combine like terms: -3.881043674 + -2.75 = -6.631043674 a = -6.631043674 Simplifying a = -6.631043674Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.131043674, -6.631043674}
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