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Simplifying 5x + 34 = 2x(1 + -7x) Reorder the terms: 34 + 5x = 2x(1 + -7x) 34 + 5x = (1 * 2x + -7x * 2x) 34 + 5x = (2x + -14x2) Solving 34 + 5x = 2x + -14x2 Solving for variable 'x'. Combine like terms: 5x + -2x = 3x 34 + 3x + 14x2 = 2x + -14x2 + -2x + 14x2 Reorder the terms: 34 + 3x + 14x2 = 2x + -2x + -14x2 + 14x2 Combine like terms: 2x + -2x = 0 34 + 3x + 14x2 = 0 + -14x2 + 14x2 34 + 3x + 14x2 = -14x2 + 14x2 Combine like terms: -14x2 + 14x2 = 0 34 + 3x + 14x2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. 2.428571429 + 0.2142857143x + x2 = 0 Move the constant term to the right: Add '-2.428571429' to each side of the equation. 2.428571429 + 0.2142857143x + -2.428571429 + x2 = 0 + -2.428571429 Reorder the terms: 2.428571429 + -2.428571429 + 0.2142857143x + x2 = 0 + -2.428571429 Combine like terms: 2.428571429 + -2.428571429 = 0.000000000 0.000000000 + 0.2142857143x + x2 = 0 + -2.428571429 0.2142857143x + x2 = 0 + -2.428571429 Combine like terms: 0 + -2.428571429 = -2.428571429 0.2142857143x + x2 = -2.428571429 The x term is 0.2142857143x. Take half its coefficient (0.1071428572). Square it (0.01147959185) and add it to both sides. Add '0.01147959185' to each side of the equation. 0.2142857143x + 0.01147959185 + x2 = -2.428571429 + 0.01147959185 Reorder the terms: 0.01147959185 + 0.2142857143x + x2 = -2.428571429 + 0.01147959185 Combine like terms: -2.428571429 + 0.01147959185 = -2.41709183715 0.01147959185 + 0.2142857143x + x2 = -2.41709183715 Factor a perfect square on the left side: (x + 0.1071428572)(x + 0.1071428572) = -2.41709183715 Can't calculate square root of the right side. The solution to this equation could not be determined.
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