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Simplifying 10y2 + 15y + 24 = (y + 5)(y + 3) Reorder the terms: 24 + 15y + 10y2 = (y + 5)(y + 3) Reorder the terms: 24 + 15y + 10y2 = (5 + y)(y + 3) Reorder the terms: 24 + 15y + 10y2 = (5 + y)(3 + y) Multiply (5 + y) * (3 + y) 24 + 15y + 10y2 = (5(3 + y) + y(3 + y)) 24 + 15y + 10y2 = ((3 * 5 + y * 5) + y(3 + y)) 24 + 15y + 10y2 = ((15 + 5y) + y(3 + y)) 24 + 15y + 10y2 = (15 + 5y + (3 * y + y * y)) 24 + 15y + 10y2 = (15 + 5y + (3y + y2)) Combine like terms: 5y + 3y = 8y 24 + 15y + 10y2 = (15 + 8y + y2) Solving 24 + 15y + 10y2 = 15 + 8y + y2 Solving for variable 'y'. Reorder the terms: 24 + -15 + 15y + -8y + 10y2 + -1y2 = 15 + 8y + y2 + -15 + -8y + -1y2 Combine like terms: 24 + -15 = 9 9 + 15y + -8y + 10y2 + -1y2 = 15 + 8y + y2 + -15 + -8y + -1y2 Combine like terms: 15y + -8y = 7y 9 + 7y + 10y2 + -1y2 = 15 + 8y + y2 + -15 + -8y + -1y2 Combine like terms: 10y2 + -1y2 = 9y2 9 + 7y + 9y2 = 15 + 8y + y2 + -15 + -8y + -1y2 Reorder the terms: 9 + 7y + 9y2 = 15 + -15 + 8y + -8y + y2 + -1y2 Combine like terms: 15 + -15 = 0 9 + 7y + 9y2 = 0 + 8y + -8y + y2 + -1y2 9 + 7y + 9y2 = 8y + -8y + y2 + -1y2 Combine like terms: 8y + -8y = 0 9 + 7y + 9y2 = 0 + y2 + -1y2 9 + 7y + 9y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 9 + 7y + 9y2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 1 + 0.7777777778y + y2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 0.7777777778y + -1 + y2 = 0 + -1 Reorder the terms: 1 + -1 + 0.7777777778y + y2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 0.7777777778y + y2 = 0 + -1 0.7777777778y + y2 = 0 + -1 Combine like terms: 0 + -1 = -1 0.7777777778y + y2 = -1 The y term is 0.7777777778y. 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. 0.7777777778y + 0.1512345679 + y2 = -1 + 0.1512345679 Reorder the terms: 0.1512345679 + 0.7777777778y + y2 = -1 + 0.1512345679 Combine like terms: -1 + 0.1512345679 = -0.8487654321 0.1512345679 + 0.7777777778y + y2 = -0.8487654321 Factor a perfect square on the left side: (y + 0.3888888889)(y + 0.3888888889) = -0.8487654321 Can't calculate square root of the right side. The solution to this equation could not be determined.
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