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Simplifying 5a2 + 17a + -49 = 0 Reorder the terms: -49 + 17a + 5a2 = 0 Solving -49 + 17a + 5a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -9.8 + 3.4a + a2 = 0 Move the constant term to the right: Add '9.8' to each side of the equation. -9.8 + 3.4a + 9.8 + a2 = 0 + 9.8 Reorder the terms: -9.8 + 9.8 + 3.4a + a2 = 0 + 9.8 Combine like terms: -9.8 + 9.8 = 0.0 0.0 + 3.4a + a2 = 0 + 9.8 3.4a + a2 = 0 + 9.8 Combine like terms: 0 + 9.8 = 9.8 3.4a + a2 = 9.8 The a term is 3.4a. Take half its coefficient (1.7). Square it (2.89) and add it to both sides. Add '2.89' to each side of the equation. 3.4a + 2.89 + a2 = 9.8 + 2.89 Reorder the terms: 2.89 + 3.4a + a2 = 9.8 + 2.89 Combine like terms: 9.8 + 2.89 = 12.69 2.89 + 3.4a + a2 = 12.69 Factor a perfect square on the left side: (a + 1.7)(a + 1.7) = 12.69 Calculate the square root of the right side: 3.562302626 Break this problem into two subproblems by setting (a + 1.7) equal to 3.562302626 and -3.562302626.Subproblem 1
a + 1.7 = 3.562302626 Simplifying a + 1.7 = 3.562302626 Reorder the terms: 1.7 + a = 3.562302626 Solving 1.7 + a = 3.562302626 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1.7' to each side of the equation. 1.7 + -1.7 + a = 3.562302626 + -1.7 Combine like terms: 1.7 + -1.7 = 0.0 0.0 + a = 3.562302626 + -1.7 a = 3.562302626 + -1.7 Combine like terms: 3.562302626 + -1.7 = 1.862302626 a = 1.862302626 Simplifying a = 1.862302626Subproblem 2
a + 1.7 = -3.562302626 Simplifying a + 1.7 = -3.562302626 Reorder the terms: 1.7 + a = -3.562302626 Solving 1.7 + a = -3.562302626 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1.7' to each side of the equation. 1.7 + -1.7 + a = -3.562302626 + -1.7 Combine like terms: 1.7 + -1.7 = 0.0 0.0 + a = -3.562302626 + -1.7 a = -3.562302626 + -1.7 Combine like terms: -3.562302626 + -1.7 = -5.262302626 a = -5.262302626 Simplifying a = -5.262302626Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.862302626, -5.262302626}
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