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Simplifying a(a + -9) = 8 Reorder the terms: a(-9 + a) = 8 (-9 * a + a * a) = 8 (-9a + a2) = 8 Solving -9a + a2 = 8 Solving for variable 'a'. Reorder the terms: -8 + -9a + a2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + -9a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + -9a + 8 + a2 = 0 + 8 Reorder the terms: -8 + 8 + -9a + a2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -9a + a2 = 0 + 8 -9a + a2 = 0 + 8 Combine like terms: 0 + 8 = 8 -9a + a2 = 8 The a term is -9a. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9a + 20.25 + a2 = 8 + 20.25 Reorder the terms: 20.25 + -9a + a2 = 8 + 20.25 Combine like terms: 8 + 20.25 = 28.25 20.25 + -9a + a2 = 28.25 Factor a perfect square on the left side: (a + -4.5)(a + -4.5) = 28.25 Calculate the square root of the right side: 5.315072906 Break this problem into two subproblems by setting (a + -4.5) equal to 5.315072906 and -5.315072906.Subproblem 1
a + -4.5 = 5.315072906 Simplifying a + -4.5 = 5.315072906 Reorder the terms: -4.5 + a = 5.315072906 Solving -4.5 + a = 5.315072906 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + a = 5.315072906 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + a = 5.315072906 + 4.5 a = 5.315072906 + 4.5 Combine like terms: 5.315072906 + 4.5 = 9.815072906 a = 9.815072906 Simplifying a = 9.815072906Subproblem 2
a + -4.5 = -5.315072906 Simplifying a + -4.5 = -5.315072906 Reorder the terms: -4.5 + a = -5.315072906 Solving -4.5 + a = -5.315072906 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + a = -5.315072906 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + a = -5.315072906 + 4.5 a = -5.315072906 + 4.5 Combine like terms: -5.315072906 + 4.5 = -0.815072906 a = -0.815072906 Simplifying a = -0.815072906Solution
The solution to the problem is based on the solutions from the subproblems. a = {9.815072906, -0.815072906}
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