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Simplifying 0.4y2 = 2y + -2.5 Reorder the terms: 0.4y2 = -2.5 + 2y Solving 0.4y2 = -2.5 + 2y Solving for variable 'y'. Reorder the terms: 2.5 + -2y + 0.4y2 = -2.5 + 2y + 2.5 + -2y Reorder the terms: 2.5 + -2y + 0.4y2 = -2.5 + 2.5 + 2y + -2y Combine like terms: -2.5 + 2.5 = 0.0 2.5 + -2y + 0.4y2 = 0.0 + 2y + -2y 2.5 + -2y + 0.4y2 = 2y + -2y Combine like terms: 2y + -2y = 0 2.5 + -2y + 0.4y2 = 0 Begin completing the square. Divide all terms by 0.4 the coefficient of the squared term: Divide each side by '0.4'. 6.25 + -5y + y2 = 0 Move the constant term to the right: Add '-6.25' to each side of the equation. 6.25 + -5y + -6.25 + y2 = 0 + -6.25 Reorder the terms: 6.25 + -6.25 + -5y + y2 = 0 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + -5y + y2 = 0 + -6.25 -5y + y2 = 0 + -6.25 Combine like terms: 0 + -6.25 = -6.25 -5y + y2 = -6.25 The y term is -5y. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5y + 6.25 + y2 = -6.25 + 6.25 Reorder the terms: 6.25 + -5y + y2 = -6.25 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 6.25 + -5y + y2 = 0.00 Factor a perfect square on the left side: (y + -2.5)(y + -2.5) = 0.00 Calculate the square root of the right side: 0.00 Break this problem into two subproblems by setting (y + -2.5) equal to 0.00 and 0.00.Subproblem 1
y + -2.5 = 0.00 Simplifying y + -2.5 = 0.00 Reorder the terms: -2.5 + y = 0.00 Solving -2.5 + y = 0.00 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + y = 0.00 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + y = 0.00 + 2.5 y = 0.00 + 2.5 Combine like terms: 0.00 + 2.5 = 2.5 y = 2.5 Simplifying y = 2.5Subproblem 2
y + -2.5 = 0.00 Simplifying y + -2.5 = 0.00 Reorder the terms: -2.5 + y = 0.00 Solving -2.5 + y = 0.00 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + y = 0.00 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + y = 0.00 + 2.5 y = 0.00 + 2.5 Combine like terms: 0.00 + 2.5 = 2.5 y = 2.5 Simplifying y = 2.5Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.5, 2.5}
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