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Simplifying a * a + -18a + -80 = 0 Multiply a * a a2 + -18a + -80 = 0 Reorder the terms: -80 + -18a + a2 = 0 Solving -80 + -18a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '80' to each side of the equation. -80 + -18a + 80 + a2 = 0 + 80 Reorder the terms: -80 + 80 + -18a + a2 = 0 + 80 Combine like terms: -80 + 80 = 0 0 + -18a + a2 = 0 + 80 -18a + a2 = 0 + 80 Combine like terms: 0 + 80 = 80 -18a + a2 = 80 The a term is -18a. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18a + 81 + a2 = 80 + 81 Reorder the terms: 81 + -18a + a2 = 80 + 81 Combine like terms: 80 + 81 = 161 81 + -18a + a2 = 161 Factor a perfect square on the left side: (a + -9)(a + -9) = 161 Calculate the square root of the right side: 12.68857754 Break this problem into two subproblems by setting (a + -9) equal to 12.68857754 and -12.68857754.Subproblem 1
a + -9 = 12.68857754 Simplifying a + -9 = 12.68857754 Reorder the terms: -9 + a = 12.68857754 Solving -9 + a = 12.68857754 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + a = 12.68857754 + 9 Combine like terms: -9 + 9 = 0 0 + a = 12.68857754 + 9 a = 12.68857754 + 9 Combine like terms: 12.68857754 + 9 = 21.68857754 a = 21.68857754 Simplifying a = 21.68857754Subproblem 2
a + -9 = -12.68857754 Simplifying a + -9 = -12.68857754 Reorder the terms: -9 + a = -12.68857754 Solving -9 + a = -12.68857754 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + a = -12.68857754 + 9 Combine like terms: -9 + 9 = 0 0 + a = -12.68857754 + 9 a = -12.68857754 + 9 Combine like terms: -12.68857754 + 9 = -3.68857754 a = -3.68857754 Simplifying a = -3.68857754Solution
The solution to the problem is based on the solutions from the subproblems. a = {21.68857754, -3.68857754}
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