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Simplifying 8 + -5(-2 + 3y) = 14 + -9y(y + 1) 8 + (-2 * -5 + 3y * -5) = 14 + -9y(y + 1) 8 + (10 + -15y) = 14 + -9y(y + 1) Combine like terms: 8 + 10 = 18 18 + -15y = 14 + -9y(y + 1) Reorder the terms: 18 + -15y = 14 + -9y(1 + y) 18 + -15y = 14 + (1 * -9y + y * -9y) 18 + -15y = 14 + (-9y + -9y2) Solving 18 + -15y = 14 + -9y + -9y2 Solving for variable 'y'. Reorder the terms: 18 + -14 + -15y + 9y + 9y2 = 14 + -9y + -9y2 + -14 + 9y + 9y2 Combine like terms: 18 + -14 = 4 4 + -15y + 9y + 9y2 = 14 + -9y + -9y2 + -14 + 9y + 9y2 Combine like terms: -15y + 9y = -6y 4 + -6y + 9y2 = 14 + -9y + -9y2 + -14 + 9y + 9y2 Reorder the terms: 4 + -6y + 9y2 = 14 + -14 + -9y + 9y + -9y2 + 9y2 Combine like terms: 14 + -14 = 0 4 + -6y + 9y2 = 0 + -9y + 9y + -9y2 + 9y2 4 + -6y + 9y2 = -9y + 9y + -9y2 + 9y2 Combine like terms: -9y + 9y = 0 4 + -6y + 9y2 = 0 + -9y2 + 9y2 4 + -6y + 9y2 = -9y2 + 9y2 Combine like terms: -9y2 + 9y2 = 0 4 + -6y + 9y2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.4444444444 + -0.6666666667y + y2 = 0 Move the constant term to the right: Add '-0.4444444444' to each side of the equation. 0.4444444444 + -0.6666666667y + -0.4444444444 + y2 = 0 + -0.4444444444 Reorder the terms: 0.4444444444 + -0.4444444444 + -0.6666666667y + y2 = 0 + -0.4444444444 Combine like terms: 0.4444444444 + -0.4444444444 = 0.0000000000 0.0000000000 + -0.6666666667y + y2 = 0 + -0.4444444444 -0.6666666667y + y2 = 0 + -0.4444444444 Combine like terms: 0 + -0.4444444444 = -0.4444444444 -0.6666666667y + y2 = -0.4444444444 The y term is -0.6666666667y. Take half its coefficient (-0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. -0.6666666667y + 0.1111111112 + y2 = -0.4444444444 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667y + y2 = -0.4444444444 + 0.1111111112 Combine like terms: -0.4444444444 + 0.1111111112 = -0.3333333332 0.1111111112 + -0.6666666667y + y2 = -0.3333333332 Factor a perfect square on the left side: (y + -0.3333333334)(y + -0.3333333334) = -0.3333333332 Can't calculate square root of the right side. The solution to this equation could not be determined.
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