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Simplifying 0.18y(y + -3) + 0.06 = 0.08y + -0.3 Reorder the terms: 0.18y(-3 + y) + 0.06 = 0.08y + -0.3 (-3 * 0.18y + y * 0.18y) + 0.06 = 0.08y + -0.3 (-0.54y + 0.18y2) + 0.06 = 0.08y + -0.3 Reorder the terms: 0.06 + -0.54y + 0.18y2 = 0.08y + -0.3 Reorder the terms: 0.06 + -0.54y + 0.18y2 = -0.3 + 0.08y Solving 0.06 + -0.54y + 0.18y2 = -0.3 + 0.08y Solving for variable 'y'. Reorder the terms: 0.06 + 0.3 + -0.54y + -0.08y + 0.18y2 = -0.3 + 0.08y + 0.3 + -0.08y Combine like terms: 0.06 + 0.3 = 0.36 0.36 + -0.54y + -0.08y + 0.18y2 = -0.3 + 0.08y + 0.3 + -0.08y Combine like terms: -0.54y + -0.08y = -0.62y 0.36 + -0.62y + 0.18y2 = -0.3 + 0.08y + 0.3 + -0.08y Reorder the terms: 0.36 + -0.62y + 0.18y2 = -0.3 + 0.3 + 0.08y + -0.08y Combine like terms: -0.3 + 0.3 = 0.0 0.36 + -0.62y + 0.18y2 = 0.0 + 0.08y + -0.08y 0.36 + -0.62y + 0.18y2 = 0.08y + -0.08y Combine like terms: 0.08y + -0.08y = 0.00 0.36 + -0.62y + 0.18y2 = 0.00 Begin completing the square. Divide all terms by 0.18 the coefficient of the squared term: Divide each side by '0.18'. 2 + -3.444444444y + y2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -3.444444444y + -2 + y2 = 0 + -2 Reorder the terms: 2 + -2 + -3.444444444y + y2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3.444444444y + y2 = 0 + -2 -3.444444444y + y2 = 0 + -2 Combine like terms: 0 + -2 = -2 -3.444444444y + y2 = -2 The y term is -3.444444444y. Take half its coefficient (-1.722222222). Square it (2.966049382) and add it to both sides. Add '2.966049382' to each side of the equation. -3.444444444y + 2.966049382 + y2 = -2 + 2.966049382 Reorder the terms: 2.966049382 + -3.444444444y + y2 = -2 + 2.966049382 Combine like terms: -2 + 2.966049382 = 0.966049382 2.966049382 + -3.444444444y + y2 = 0.966049382 Factor a perfect square on the left side: (y + -1.722222222)(y + -1.722222222) = 0.966049382 Calculate the square root of the right side: 0.982878111 Break this problem into two subproblems by setting (y + -1.722222222) equal to 0.982878111 and -0.982878111.Subproblem 1
y + -1.722222222 = 0.982878111 Simplifying y + -1.722222222 = 0.982878111 Reorder the terms: -1.722222222 + y = 0.982878111 Solving -1.722222222 + y = 0.982878111 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.722222222' to each side of the equation. -1.722222222 + 1.722222222 + y = 0.982878111 + 1.722222222 Combine like terms: -1.722222222 + 1.722222222 = 0.000000000 0.000000000 + y = 0.982878111 + 1.722222222 y = 0.982878111 + 1.722222222 Combine like terms: 0.982878111 + 1.722222222 = 2.705100333 y = 2.705100333 Simplifying y = 2.705100333Subproblem 2
y + -1.722222222 = -0.982878111 Simplifying y + -1.722222222 = -0.982878111 Reorder the terms: -1.722222222 + y = -0.982878111 Solving -1.722222222 + y = -0.982878111 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.722222222' to each side of the equation. -1.722222222 + 1.722222222 + y = -0.982878111 + 1.722222222 Combine like terms: -1.722222222 + 1.722222222 = 0.000000000 0.000000000 + y = -0.982878111 + 1.722222222 y = -0.982878111 + 1.722222222 Combine like terms: -0.982878111 + 1.722222222 = 0.739344111 y = 0.739344111 Simplifying y = 0.739344111Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.705100333, 0.739344111}
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