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Simplifying 2a2 + -18a + -27 = 0 Reorder the terms: -27 + -18a + 2a2 = 0 Solving -27 + -18a + 2a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -13.5 + -9a + a2 = 0 Move the constant term to the right: Add '13.5' to each side of the equation. -13.5 + -9a + 13.5 + a2 = 0 + 13.5 Reorder the terms: -13.5 + 13.5 + -9a + a2 = 0 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + -9a + a2 = 0 + 13.5 -9a + a2 = 0 + 13.5 Combine like terms: 0 + 13.5 = 13.5 -9a + a2 = 13.5 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 = 13.5 + 20.25 Reorder the terms: 20.25 + -9a + a2 = 13.5 + 20.25 Combine like terms: 13.5 + 20.25 = 33.75 20.25 + -9a + a2 = 33.75 Factor a perfect square on the left side: (a + -4.5)(a + -4.5) = 33.75 Calculate the square root of the right side: 5.809475019 Break this problem into two subproblems by setting (a + -4.5) equal to 5.809475019 and -5.809475019.Subproblem 1
a + -4.5 = 5.809475019 Simplifying a + -4.5 = 5.809475019 Reorder the terms: -4.5 + a = 5.809475019 Solving -4.5 + a = 5.809475019 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 = 5.809475019 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + a = 5.809475019 + 4.5 a = 5.809475019 + 4.5 Combine like terms: 5.809475019 + 4.5 = 10.309475019 a = 10.309475019 Simplifying a = 10.309475019Subproblem 2
a + -4.5 = -5.809475019 Simplifying a + -4.5 = -5.809475019 Reorder the terms: -4.5 + a = -5.809475019 Solving -4.5 + a = -5.809475019 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 = -5.809475019 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + a = -5.809475019 + 4.5 a = -5.809475019 + 4.5 Combine like terms: -5.809475019 + 4.5 = -1.309475019 a = -1.309475019 Simplifying a = -1.309475019Solution
The solution to the problem is based on the solutions from the subproblems. a = {10.309475019, -1.309475019}
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