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Simplifying 3x(3x + 1) = 5(2x + -7) Reorder the terms: 3x(1 + 3x) = 5(2x + -7) (1 * 3x + 3x * 3x) = 5(2x + -7) (3x + 9x2) = 5(2x + -7) Reorder the terms: 3x + 9x2 = 5(-7 + 2x) 3x + 9x2 = (-7 * 5 + 2x * 5) 3x + 9x2 = (-35 + 10x) Solving 3x + 9x2 = -35 + 10x Solving for variable 'x'. Reorder the terms: 35 + 3x + -10x + 9x2 = -35 + 10x + 35 + -10x Combine like terms: 3x + -10x = -7x 35 + -7x + 9x2 = -35 + 10x + 35 + -10x Reorder the terms: 35 + -7x + 9x2 = -35 + 35 + 10x + -10x Combine like terms: -35 + 35 = 0 35 + -7x + 9x2 = 0 + 10x + -10x 35 + -7x + 9x2 = 10x + -10x Combine like terms: 10x + -10x = 0 35 + -7x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 3.888888889 + -0.7777777778x + x2 = 0 Move the constant term to the right: Add '-3.888888889' to each side of the equation. 3.888888889 + -0.7777777778x + -3.888888889 + x2 = 0 + -3.888888889 Reorder the terms: 3.888888889 + -3.888888889 + -0.7777777778x + x2 = 0 + -3.888888889 Combine like terms: 3.888888889 + -3.888888889 = 0.000000000 0.000000000 + -0.7777777778x + x2 = 0 + -3.888888889 -0.7777777778x + x2 = 0 + -3.888888889 Combine like terms: 0 + -3.888888889 = -3.888888889 -0.7777777778x + x2 = -3.888888889 The x term is -0.7777777778x. Take half its coefficient (-0.3888888889). Square it (0.1512345679) and add it to both sides. Add '0.1512345679' to each side of the equation. -0.7777777778x + 0.1512345679 + x2 = -3.888888889 + 0.1512345679 Reorder the terms: 0.1512345679 + -0.7777777778x + x2 = -3.888888889 + 0.1512345679 Combine like terms: -3.888888889 + 0.1512345679 = -3.7376543211 0.1512345679 + -0.7777777778x + x2 = -3.7376543211 Factor a perfect square on the left side: (x + -0.3888888889)(x + -0.3888888889) = -3.7376543211 Can't calculate square root of the right side. The solution to this equation could not be determined.
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