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Simplifying 5a2 + -8a = 15 Reorder the terms: -8a + 5a2 = 15 Solving -8a + 5a2 = 15 Solving for variable 'a'. Reorder the terms: -15 + -8a + 5a2 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + -8a + 5a2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3 + -1.6a + a2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -1.6a + 3 + a2 = 0 + 3 Reorder the terms: -3 + 3 + -1.6a + a2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1.6a + a2 = 0 + 3 -1.6a + a2 = 0 + 3 Combine like terms: 0 + 3 = 3 -1.6a + a2 = 3 The a term is -1.6a. Take half its coefficient (-0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. -1.6a + 0.64 + a2 = 3 + 0.64 Reorder the terms: 0.64 + -1.6a + a2 = 3 + 0.64 Combine like terms: 3 + 0.64 = 3.64 0.64 + -1.6a + a2 = 3.64 Factor a perfect square on the left side: (a + -0.8)(a + -0.8) = 3.64 Calculate the square root of the right side: 1.907878403 Break this problem into two subproblems by setting (a + -0.8) equal to 1.907878403 and -1.907878403.Subproblem 1
a + -0.8 = 1.907878403 Simplifying a + -0.8 = 1.907878403 Reorder the terms: -0.8 + a = 1.907878403 Solving -0.8 + a = 1.907878403 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + a = 1.907878403 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + a = 1.907878403 + 0.8 a = 1.907878403 + 0.8 Combine like terms: 1.907878403 + 0.8 = 2.707878403 a = 2.707878403 Simplifying a = 2.707878403Subproblem 2
a + -0.8 = -1.907878403 Simplifying a + -0.8 = -1.907878403 Reorder the terms: -0.8 + a = -1.907878403 Solving -0.8 + a = -1.907878403 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + a = -1.907878403 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + a = -1.907878403 + 0.8 a = -1.907878403 + 0.8 Combine like terms: -1.907878403 + 0.8 = -1.107878403 a = -1.107878403 Simplifying a = -1.107878403Solution
The solution to the problem is based on the solutions from the subproblems. a = {2.707878403, -1.107878403}
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