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Simplifying 0.02(y + -1) * 0.20y = 0.08y + -0.3 Reorder the terms: 0.02(-1 + y) * 0.20y = 0.08y + -0.3 Reorder the terms for easier multiplication: 0.02 * 0.20y(-1 + y) = 0.08y + -0.3 Multiply 0.02 * 0.20 0.004y(-1 + y) = 0.08y + -0.3 (-1 * 0.004y + y * 0.004y) = 0.08y + -0.3 (-0.004y + 0.004y2) = 0.08y + -0.3 Reorder the terms: -0.004y + 0.004y2 = -0.3 + 0.08y Solving -0.004y + 0.004y2 = -0.3 + 0.08y Solving for variable 'y'. Reorder the terms: 0.3 + -0.004y + -0.08y + 0.004y2 = -0.3 + 0.08y + 0.3 + -0.08y Combine like terms: -0.004y + -0.08y = -0.084y 0.3 + -0.084y + 0.004y2 = -0.3 + 0.08y + 0.3 + -0.08y Reorder the terms: 0.3 + -0.084y + 0.004y2 = -0.3 + 0.3 + 0.08y + -0.08y Combine like terms: -0.3 + 0.3 = 0.0 0.3 + -0.084y + 0.004y2 = 0.0 + 0.08y + -0.08y 0.3 + -0.084y + 0.004y2 = 0.08y + -0.08y Combine like terms: 0.08y + -0.08y = 0.00 0.3 + -0.084y + 0.004y2 = 0.00 Begin completing the square. Divide all terms by 0.004 the coefficient of the squared term: Divide each side by '0.004'. 75 + -21y + y2 = 0 Move the constant term to the right: Add '-75' to each side of the equation. 75 + -21y + -75 + y2 = 0 + -75 Reorder the terms: 75 + -75 + -21y + y2 = 0 + -75 Combine like terms: 75 + -75 = 0 0 + -21y + y2 = 0 + -75 -21y + y2 = 0 + -75 Combine like terms: 0 + -75 = -75 -21y + y2 = -75 The y term is -21y. Take half its coefficient (-10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. -21y + 110.25 + y2 = -75 + 110.25 Reorder the terms: 110.25 + -21y + y2 = -75 + 110.25 Combine like terms: -75 + 110.25 = 35.25 110.25 + -21y + y2 = 35.25 Factor a perfect square on the left side: (y + -10.5)(y + -10.5) = 35.25 Calculate the square root of the right side: 5.937171044 Break this problem into two subproblems by setting (y + -10.5) equal to 5.937171044 and -5.937171044.Subproblem 1
y + -10.5 = 5.937171044 Simplifying y + -10.5 = 5.937171044 Reorder the terms: -10.5 + y = 5.937171044 Solving -10.5 + y = 5.937171044 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + y = 5.937171044 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + y = 5.937171044 + 10.5 y = 5.937171044 + 10.5 Combine like terms: 5.937171044 + 10.5 = 16.437171044 y = 16.437171044 Simplifying y = 16.437171044Subproblem 2
y + -10.5 = -5.937171044 Simplifying y + -10.5 = -5.937171044 Reorder the terms: -10.5 + y = -5.937171044 Solving -10.5 + y = -5.937171044 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + y = -5.937171044 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + y = -5.937171044 + 10.5 y = -5.937171044 + 10.5 Combine like terms: -5.937171044 + 10.5 = 4.562828956 y = 4.562828956 Simplifying y = 4.562828956Solution
The solution to the problem is based on the solutions from the subproblems. y = {16.437171044, 4.562828956}
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