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Simplifying 9a2 + -18a + -47 = 0 Reorder the terms: -47 + -18a + 9a2 = 0 Solving -47 + -18a + 9a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -5.222222222 + -2a + a2 = 0 Move the constant term to the right: Add '5.222222222' to each side of the equation. -5.222222222 + -2a + 5.222222222 + a2 = 0 + 5.222222222 Reorder the terms: -5.222222222 + 5.222222222 + -2a + a2 = 0 + 5.222222222 Combine like terms: -5.222222222 + 5.222222222 = 0.000000000 0.000000000 + -2a + a2 = 0 + 5.222222222 -2a + a2 = 0 + 5.222222222 Combine like terms: 0 + 5.222222222 = 5.222222222 -2a + a2 = 5.222222222 The a term is -2a. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2a + 1 + a2 = 5.222222222 + 1 Reorder the terms: 1 + -2a + a2 = 5.222222222 + 1 Combine like terms: 5.222222222 + 1 = 6.222222222 1 + -2a + a2 = 6.222222222 Factor a perfect square on the left side: (a + -1)(a + -1) = 6.222222222 Calculate the square root of the right side: 2.494438258 Break this problem into two subproblems by setting (a + -1) equal to 2.494438258 and -2.494438258.Subproblem 1
a + -1 = 2.494438258 Simplifying a + -1 = 2.494438258 Reorder the terms: -1 + a = 2.494438258 Solving -1 + a = 2.494438258 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + a = 2.494438258 + 1 Combine like terms: -1 + 1 = 0 0 + a = 2.494438258 + 1 a = 2.494438258 + 1 Combine like terms: 2.494438258 + 1 = 3.494438258 a = 3.494438258 Simplifying a = 3.494438258Subproblem 2
a + -1 = -2.494438258 Simplifying a + -1 = -2.494438258 Reorder the terms: -1 + a = -2.494438258 Solving -1 + a = -2.494438258 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + a = -2.494438258 + 1 Combine like terms: -1 + 1 = 0 0 + a = -2.494438258 + 1 a = -2.494438258 + 1 Combine like terms: -2.494438258 + 1 = -1.494438258 a = -1.494438258 Simplifying a = -1.494438258Solution
The solution to the problem is based on the solutions from the subproblems. a = {3.494438258, -1.494438258}
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