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Simplifying (3y + 5)(3y + 5) + (y + -4)(y + -4) = 6y Reorder the terms: (5 + 3y)(3y + 5) + (y + -4)(y + -4) = 6y Reorder the terms: (5 + 3y)(5 + 3y) + (y + -4)(y + -4) = 6y Multiply (5 + 3y) * (5 + 3y) (5(5 + 3y) + 3y * (5 + 3y)) + (y + -4)(y + -4) = 6y ((5 * 5 + 3y * 5) + 3y * (5 + 3y)) + (y + -4)(y + -4) = 6y ((25 + 15y) + 3y * (5 + 3y)) + (y + -4)(y + -4) = 6y (25 + 15y + (5 * 3y + 3y * 3y)) + (y + -4)(y + -4) = 6y (25 + 15y + (15y + 9y2)) + (y + -4)(y + -4) = 6y Combine like terms: 15y + 15y = 30y (25 + 30y + 9y2) + (y + -4)(y + -4) = 6y Reorder the terms: 25 + 30y + 9y2 + (-4 + y)(y + -4) = 6y Reorder the terms: 25 + 30y + 9y2 + (-4 + y)(-4 + y) = 6y Multiply (-4 + y) * (-4 + y) 25 + 30y + 9y2 + (-4(-4 + y) + y(-4 + y)) = 6y 25 + 30y + 9y2 + ((-4 * -4 + y * -4) + y(-4 + y)) = 6y 25 + 30y + 9y2 + ((16 + -4y) + y(-4 + y)) = 6y 25 + 30y + 9y2 + (16 + -4y + (-4 * y + y * y)) = 6y 25 + 30y + 9y2 + (16 + -4y + (-4y + y2)) = 6y Combine like terms: -4y + -4y = -8y 25 + 30y + 9y2 + (16 + -8y + y2) = 6y Reorder the terms: 25 + 16 + 30y + -8y + 9y2 + y2 = 6y Combine like terms: 25 + 16 = 41 41 + 30y + -8y + 9y2 + y2 = 6y Combine like terms: 30y + -8y = 22y 41 + 22y + 9y2 + y2 = 6y Combine like terms: 9y2 + y2 = 10y2 41 + 22y + 10y2 = 6y Solving 41 + 22y + 10y2 = 6y Solving for variable 'y'. Reorder the terms: 41 + 22y + -6y + 10y2 = 6y + -6y Combine like terms: 22y + -6y = 16y 41 + 16y + 10y2 = 6y + -6y Combine like terms: 6y + -6y = 0 41 + 16y + 10y2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 4.1 + 1.6y + y2 = 0.0 Move the constant term to the right: Add '-4.1' to each side of the equation. 4.1 + 1.6y + -4.1 + y2 = 0.0 + -4.1 Reorder the terms: 4.1 + -4.1 + 1.6y + y2 = 0.0 + -4.1 Combine like terms: 4.1 + -4.1 = 0.0 0.0 + 1.6y + y2 = 0.0 + -4.1 1.6y + y2 = 0.0 + -4.1 Combine like terms: 0.0 + -4.1 = -4.1 1.6y + y2 = -4.1 The y term is 1.6y. Take half its coefficient (0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. 1.6y + 0.64 + y2 = -4.1 + 0.64 Reorder the terms: 0.64 + 1.6y + y2 = -4.1 + 0.64 Combine like terms: -4.1 + 0.64 = -3.46 0.64 + 1.6y + y2 = -3.46 Factor a perfect square on the left side: (y + 0.8)(y + 0.8) = -3.46 Can't calculate square root of the right side. The solution to this equation could not be determined.
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