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Simplifying a2 + -18a + 9 = 0 Reorder the terms: 9 + -18a + a2 = 0 Solving 9 + -18a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + -18a + -9 + a2 = 0 + -9 Reorder the terms: 9 + -9 + -18a + a2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -18a + a2 = 0 + -9 -18a + a2 = 0 + -9 Combine like terms: 0 + -9 = -9 -18a + a2 = -9 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 = -9 + 81 Reorder the terms: 81 + -18a + a2 = -9 + 81 Combine like terms: -9 + 81 = 72 81 + -18a + a2 = 72 Factor a perfect square on the left side: (a + -9)(a + -9) = 72 Calculate the square root of the right side: 8.485281374 Break this problem into two subproblems by setting (a + -9) equal to 8.485281374 and -8.485281374.Subproblem 1
a + -9 = 8.485281374 Simplifying a + -9 = 8.485281374 Reorder the terms: -9 + a = 8.485281374 Solving -9 + a = 8.485281374 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 = 8.485281374 + 9 Combine like terms: -9 + 9 = 0 0 + a = 8.485281374 + 9 a = 8.485281374 + 9 Combine like terms: 8.485281374 + 9 = 17.485281374 a = 17.485281374 Simplifying a = 17.485281374Subproblem 2
a + -9 = -8.485281374 Simplifying a + -9 = -8.485281374 Reorder the terms: -9 + a = -8.485281374 Solving -9 + a = -8.485281374 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 = -8.485281374 + 9 Combine like terms: -9 + 9 = 0 0 + a = -8.485281374 + 9 a = -8.485281374 + 9 Combine like terms: -8.485281374 + 9 = 0.514718626 a = 0.514718626 Simplifying a = 0.514718626Solution
The solution to the problem is based on the solutions from the subproblems. a = {17.485281374, 0.514718626}
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