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Simplifying 8a2 + 6a = 15 Reorder the terms: 6a + 8a2 = 15 Solving 6a + 8a2 = 15 Solving for variable 'a'. Reorder the terms: -15 + 6a + 8a2 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + 6a + 8a2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.875 + 0.75a + a2 = 0 Move the constant term to the right: Add '1.875' to each side of the equation. -1.875 + 0.75a + 1.875 + a2 = 0 + 1.875 Reorder the terms: -1.875 + 1.875 + 0.75a + a2 = 0 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + 0.75a + a2 = 0 + 1.875 0.75a + a2 = 0 + 1.875 Combine like terms: 0 + 1.875 = 1.875 0.75a + a2 = 1.875 The a term is 0.75a. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75a + 0.140625 + a2 = 1.875 + 0.140625 Reorder the terms: 0.140625 + 0.75a + a2 = 1.875 + 0.140625 Combine like terms: 1.875 + 0.140625 = 2.015625 0.140625 + 0.75a + a2 = 2.015625 Factor a perfect square on the left side: (a + 0.375)(a + 0.375) = 2.015625 Calculate the square root of the right side: 1.419727086 Break this problem into two subproblems by setting (a + 0.375) equal to 1.419727086 and -1.419727086.Subproblem 1
a + 0.375 = 1.419727086 Simplifying a + 0.375 = 1.419727086 Reorder the terms: 0.375 + a = 1.419727086 Solving 0.375 + a = 1.419727086 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + a = 1.419727086 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + a = 1.419727086 + -0.375 a = 1.419727086 + -0.375 Combine like terms: 1.419727086 + -0.375 = 1.044727086 a = 1.044727086 Simplifying a = 1.044727086Subproblem 2
a + 0.375 = -1.419727086 Simplifying a + 0.375 = -1.419727086 Reorder the terms: 0.375 + a = -1.419727086 Solving 0.375 + a = -1.419727086 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + a = -1.419727086 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + a = -1.419727086 + -0.375 a = -1.419727086 + -0.375 Combine like terms: -1.419727086 + -0.375 = -1.794727086 a = -1.794727086 Simplifying a = -1.794727086Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.044727086, -1.794727086}
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