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Simplifying 2a2 + -27a + 72 = 0 Reorder the terms: 72 + -27a + 2a2 = 0 Solving 72 + -27a + 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'. 36 + -13.5a + a2 = 0 Move the constant term to the right: Add '-36' to each side of the equation. 36 + -13.5a + -36 + a2 = 0 + -36 Reorder the terms: 36 + -36 + -13.5a + a2 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + -13.5a + a2 = 0 + -36 -13.5a + a2 = 0 + -36 Combine like terms: 0 + -36 = -36 -13.5a + a2 = -36 The a term is -13.5a. Take half its coefficient (-6.75). Square it (45.5625) and add it to both sides. Add '45.5625' to each side of the equation. -13.5a + 45.5625 + a2 = -36 + 45.5625 Reorder the terms: 45.5625 + -13.5a + a2 = -36 + 45.5625 Combine like terms: -36 + 45.5625 = 9.5625 45.5625 + -13.5a + a2 = 9.5625 Factor a perfect square on the left side: (a + -6.75)(a + -6.75) = 9.5625 Calculate the square root of the right side: 3.092329219 Break this problem into two subproblems by setting (a + -6.75) equal to 3.092329219 and -3.092329219.Subproblem 1
a + -6.75 = 3.092329219 Simplifying a + -6.75 = 3.092329219 Reorder the terms: -6.75 + a = 3.092329219 Solving -6.75 + a = 3.092329219 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '6.75' to each side of the equation. -6.75 + 6.75 + a = 3.092329219 + 6.75 Combine like terms: -6.75 + 6.75 = 0.00 0.00 + a = 3.092329219 + 6.75 a = 3.092329219 + 6.75 Combine like terms: 3.092329219 + 6.75 = 9.842329219 a = 9.842329219 Simplifying a = 9.842329219Subproblem 2
a + -6.75 = -3.092329219 Simplifying a + -6.75 = -3.092329219 Reorder the terms: -6.75 + a = -3.092329219 Solving -6.75 + a = -3.092329219 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '6.75' to each side of the equation. -6.75 + 6.75 + a = -3.092329219 + 6.75 Combine like terms: -6.75 + 6.75 = 0.00 0.00 + a = -3.092329219 + 6.75 a = -3.092329219 + 6.75 Combine like terms: -3.092329219 + 6.75 = 3.657670781 a = 3.657670781 Simplifying a = 3.657670781Solution
The solution to the problem is based on the solutions from the subproblems. a = {9.842329219, 3.657670781}
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