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Simplifying 27x2 + -20x + -6 = 0 Reorder the terms: -6 + -20x + 27x2 = 0 Solving -6 + -20x + 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'. -0.2222222222 + -0.7407407407x + x2 = 0 Move the constant term to the right: Add '0.2222222222' to each side of the equation. -0.2222222222 + -0.7407407407x + 0.2222222222 + x2 = 0 + 0.2222222222 Reorder the terms: -0.2222222222 + 0.2222222222 + -0.7407407407x + x2 = 0 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + -0.7407407407x + x2 = 0 + 0.2222222222 -0.7407407407x + x2 = 0 + 0.2222222222 Combine like terms: 0 + 0.2222222222 = 0.2222222222 -0.7407407407x + x2 = 0.2222222222 The x term is -0.7407407407x. Take half its coefficient (-0.3703703704). Square it (0.1371742113) and add it to both sides. Add '0.1371742113' to each side of the equation. -0.7407407407x + 0.1371742113 + x2 = 0.2222222222 + 0.1371742113 Reorder the terms: 0.1371742113 + -0.7407407407x + x2 = 0.2222222222 + 0.1371742113 Combine like terms: 0.2222222222 + 0.1371742113 = 0.3593964335 0.1371742113 + -0.7407407407x + x2 = 0.3593964335 Factor a perfect square on the left side: (x + -0.3703703704)(x + -0.3703703704) = 0.3593964335 Calculate the square root of the right side: 0.599496817 Break this problem into two subproblems by setting (x + -0.3703703704) equal to 0.599496817 and -0.599496817.Subproblem 1
x + -0.3703703704 = 0.599496817 Simplifying x + -0.3703703704 = 0.599496817 Reorder the terms: -0.3703703704 + x = 0.599496817 Solving -0.3703703704 + x = 0.599496817 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3703703704' to each side of the equation. -0.3703703704 + 0.3703703704 + x = 0.599496817 + 0.3703703704 Combine like terms: -0.3703703704 + 0.3703703704 = 0.0000000000 0.0000000000 + x = 0.599496817 + 0.3703703704 x = 0.599496817 + 0.3703703704 Combine like terms: 0.599496817 + 0.3703703704 = 0.9698671874 x = 0.9698671874 Simplifying x = 0.9698671874Subproblem 2
x + -0.3703703704 = -0.599496817 Simplifying x + -0.3703703704 = -0.599496817 Reorder the terms: -0.3703703704 + x = -0.599496817 Solving -0.3703703704 + x = -0.599496817 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3703703704' to each side of the equation. -0.3703703704 + 0.3703703704 + x = -0.599496817 + 0.3703703704 Combine like terms: -0.3703703704 + 0.3703703704 = 0.0000000000 0.0000000000 + x = -0.599496817 + 0.3703703704 x = -0.599496817 + 0.3703703704 Combine like terms: -0.599496817 + 0.3703703704 = -0.2291264466 x = -0.2291264466 Simplifying x = -0.2291264466Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9698671874, -0.2291264466}
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