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Simplifying 27x2 + -300x + -65 = 0 Reorder the terms: -65 + -300x + 27x2 = 0 Solving -65 + -300x + 27x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 27 the coefficient of the squared term: Divide each side by '27'. -2.407407407 + -11.11111111x + x2 = 0 Move the constant term to the right: Add '2.407407407' to each side of the equation. -2.407407407 + -11.11111111x + 2.407407407 + x2 = 0 + 2.407407407 Reorder the terms: -2.407407407 + 2.407407407 + -11.11111111x + x2 = 0 + 2.407407407 Combine like terms: -2.407407407 + 2.407407407 = 0.000000000 0.000000000 + -11.11111111x + x2 = 0 + 2.407407407 -11.11111111x + x2 = 0 + 2.407407407 Combine like terms: 0 + 2.407407407 = 2.407407407 -11.11111111x + x2 = 2.407407407 The x term is -11.11111111x. Take half its coefficient (-5.555555555). Square it (30.86419752) and add it to both sides. Add '30.86419752' to each side of the equation. -11.11111111x + 30.86419752 + x2 = 2.407407407 + 30.86419752 Reorder the terms: 30.86419752 + -11.11111111x + x2 = 2.407407407 + 30.86419752 Combine like terms: 2.407407407 + 30.86419752 = 33.271604927 30.86419752 + -11.11111111x + x2 = 33.271604927 Factor a perfect square on the left side: (x + -5.555555555)(x + -5.555555555) = 33.271604927 Calculate the square root of the right side: 5.768154378 Break this problem into two subproblems by setting (x + -5.555555555) equal to 5.768154378 and -5.768154378.Subproblem 1
x + -5.555555555 = 5.768154378 Simplifying x + -5.555555555 = 5.768154378 Reorder the terms: -5.555555555 + x = 5.768154378 Solving -5.555555555 + x = 5.768154378 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.555555555' to each side of the equation. -5.555555555 + 5.555555555 + x = 5.768154378 + 5.555555555 Combine like terms: -5.555555555 + 5.555555555 = 0.000000000 0.000000000 + x = 5.768154378 + 5.555555555 x = 5.768154378 + 5.555555555 Combine like terms: 5.768154378 + 5.555555555 = 11.323709933 x = 11.323709933 Simplifying x = 11.323709933Subproblem 2
x + -5.555555555 = -5.768154378 Simplifying x + -5.555555555 = -5.768154378 Reorder the terms: -5.555555555 + x = -5.768154378 Solving -5.555555555 + x = -5.768154378 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.555555555' to each side of the equation. -5.555555555 + 5.555555555 + x = -5.768154378 + 5.555555555 Combine like terms: -5.555555555 + 5.555555555 = 0.000000000 0.000000000 + x = -5.768154378 + 5.555555555 x = -5.768154378 + 5.555555555 Combine like terms: -5.768154378 + 5.555555555 = -0.212598823 x = -0.212598823 Simplifying x = -0.212598823Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.323709933, -0.212598823}
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