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Simplifying 15a2 + 51a + -26 = 0 Reorder the terms: -26 + 51a + 15a2 = 0 Solving -26 + 51a + 15a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -1.733333333 + 3.4a + a2 = 0 Move the constant term to the right: Add '1.733333333' to each side of the equation. -1.733333333 + 3.4a + 1.733333333 + a2 = 0 + 1.733333333 Reorder the terms: -1.733333333 + 1.733333333 + 3.4a + a2 = 0 + 1.733333333 Combine like terms: -1.733333333 + 1.733333333 = 0.000000000 0.000000000 + 3.4a + a2 = 0 + 1.733333333 3.4a + a2 = 0 + 1.733333333 Combine like terms: 0 + 1.733333333 = 1.733333333 3.4a + a2 = 1.733333333 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 = 1.733333333 + 2.89 Reorder the terms: 2.89 + 3.4a + a2 = 1.733333333 + 2.89 Combine like terms: 1.733333333 + 2.89 = 4.623333333 2.89 + 3.4a + a2 = 4.623333333 Factor a perfect square on the left side: (a + 1.7)(a + 1.7) = 4.623333333 Calculate the square root of the right side: 2.15019379 Break this problem into two subproblems by setting (a + 1.7) equal to 2.15019379 and -2.15019379.Subproblem 1
a + 1.7 = 2.15019379 Simplifying a + 1.7 = 2.15019379 Reorder the terms: 1.7 + a = 2.15019379 Solving 1.7 + a = 2.15019379 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 = 2.15019379 + -1.7 Combine like terms: 1.7 + -1.7 = 0.0 0.0 + a = 2.15019379 + -1.7 a = 2.15019379 + -1.7 Combine like terms: 2.15019379 + -1.7 = 0.45019379 a = 0.45019379 Simplifying a = 0.45019379Subproblem 2
a + 1.7 = -2.15019379 Simplifying a + 1.7 = -2.15019379 Reorder the terms: 1.7 + a = -2.15019379 Solving 1.7 + a = -2.15019379 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 = -2.15019379 + -1.7 Combine like terms: 1.7 + -1.7 = 0.0 0.0 + a = -2.15019379 + -1.7 a = -2.15019379 + -1.7 Combine like terms: -2.15019379 + -1.7 = -3.85019379 a = -3.85019379 Simplifying a = -3.85019379Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.45019379, -3.85019379}
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