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Simplifying 2x + 1 = 9x2 + 81 + 54x Reorder the terms: 1 + 2x = 9x2 + 81 + 54x Reorder the terms: 1 + 2x = 81 + 54x + 9x2 Solving 1 + 2x = 81 + 54x + 9x2 Solving for variable 'x'. Reorder the terms: 1 + -81 + 2x + -54x + -9x2 = 81 + 54x + 9x2 + -81 + -54x + -9x2 Combine like terms: 1 + -81 = -80 -80 + 2x + -54x + -9x2 = 81 + 54x + 9x2 + -81 + -54x + -9x2 Combine like terms: 2x + -54x = -52x -80 + -52x + -9x2 = 81 + 54x + 9x2 + -81 + -54x + -9x2 Reorder the terms: -80 + -52x + -9x2 = 81 + -81 + 54x + -54x + 9x2 + -9x2 Combine like terms: 81 + -81 = 0 -80 + -52x + -9x2 = 0 + 54x + -54x + 9x2 + -9x2 -80 + -52x + -9x2 = 54x + -54x + 9x2 + -9x2 Combine like terms: 54x + -54x = 0 -80 + -52x + -9x2 = 0 + 9x2 + -9x2 -80 + -52x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 -80 + -52x + -9x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(80 + 52x + 9x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(80 + 52x + 9x2)' equal to zero and attempt to solve: Simplifying 80 + 52x + 9x2 = 0 Solving 80 + 52x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 8.888888889 + 5.777777778x + x2 = 0 Move the constant term to the right: Add '-8.888888889' to each side of the equation. 8.888888889 + 5.777777778x + -8.888888889 + x2 = 0 + -8.888888889 Reorder the terms: 8.888888889 + -8.888888889 + 5.777777778x + x2 = 0 + -8.888888889 Combine like terms: 8.888888889 + -8.888888889 = 0.000000000 0.000000000 + 5.777777778x + x2 = 0 + -8.888888889 5.777777778x + x2 = 0 + -8.888888889 Combine like terms: 0 + -8.888888889 = -8.888888889 5.777777778x + x2 = -8.888888889 The x term is 5.777777778x. Take half its coefficient (2.888888889). Square it (8.345679013) and add it to both sides. Add '8.345679013' to each side of the equation. 5.777777778x + 8.345679013 + x2 = -8.888888889 + 8.345679013 Reorder the terms: 8.345679013 + 5.777777778x + x2 = -8.888888889 + 8.345679013 Combine like terms: -8.888888889 + 8.345679013 = -0.543209876 8.345679013 + 5.777777778x + x2 = -0.543209876 Factor a perfect square on the left side: (x + 2.888888889)(x + 2.888888889) = -0.543209876 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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