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Simplifying a2 + -9a + -38 = -9 Reorder the terms: -38 + -9a + a2 = -9 Solving -38 + -9a + a2 = -9 Solving for variable 'a'. Reorder the terms: -38 + 9 + -9a + a2 = -9 + 9 Combine like terms: -38 + 9 = -29 -29 + -9a + a2 = -9 + 9 Combine like terms: -9 + 9 = 0 -29 + -9a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '29' to each side of the equation. -29 + -9a + 29 + a2 = 0 + 29 Reorder the terms: -29 + 29 + -9a + a2 = 0 + 29 Combine like terms: -29 + 29 = 0 0 + -9a + a2 = 0 + 29 -9a + a2 = 0 + 29 Combine like terms: 0 + 29 = 29 -9a + a2 = 29 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 = 29 + 20.25 Reorder the terms: 20.25 + -9a + a2 = 29 + 20.25 Combine like terms: 29 + 20.25 = 49.25 20.25 + -9a + a2 = 49.25 Factor a perfect square on the left side: (a + -4.5)(a + -4.5) = 49.25 Calculate the square root of the right side: 7.017834424 Break this problem into two subproblems by setting (a + -4.5) equal to 7.017834424 and -7.017834424.Subproblem 1
a + -4.5 = 7.017834424 Simplifying a + -4.5 = 7.017834424 Reorder the terms: -4.5 + a = 7.017834424 Solving -4.5 + a = 7.017834424 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 = 7.017834424 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + a = 7.017834424 + 4.5 a = 7.017834424 + 4.5 Combine like terms: 7.017834424 + 4.5 = 11.517834424 a = 11.517834424 Simplifying a = 11.517834424Subproblem 2
a + -4.5 = -7.017834424 Simplifying a + -4.5 = -7.017834424 Reorder the terms: -4.5 + a = -7.017834424 Solving -4.5 + a = -7.017834424 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 = -7.017834424 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + a = -7.017834424 + 4.5 a = -7.017834424 + 4.5 Combine like terms: -7.017834424 + 4.5 = -2.517834424 a = -2.517834424 Simplifying a = -2.517834424Solution
The solution to the problem is based on the solutions from the subproblems. a = {11.517834424, -2.517834424}
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