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Simplifying 18 + -5y = y2 Solving 18 + -5y = y2 Solving for variable 'y'. Combine like terms: y2 + -1y2 = 0 18 + -5y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -18 + 5y + y2 = 0 Move the constant term to the right: Add '18' to each side of the equation. -18 + 5y + 18 + y2 = 0 + 18 Reorder the terms: -18 + 18 + 5y + y2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + 5y + y2 = 0 + 18 5y + y2 = 0 + 18 Combine like terms: 0 + 18 = 18 5y + y2 = 18 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 = 18 + 6.25 Reorder the terms: 6.25 + 5y + y2 = 18 + 6.25 Combine like terms: 18 + 6.25 = 24.25 6.25 + 5y + y2 = 24.25 Factor a perfect square on the left side: (y + 2.5)(y + 2.5) = 24.25 Calculate the square root of the right side: 4.924428901 Break this problem into two subproblems by setting (y + 2.5) equal to 4.924428901 and -4.924428901.Subproblem 1
y + 2.5 = 4.924428901 Simplifying y + 2.5 = 4.924428901 Reorder the terms: 2.5 + y = 4.924428901 Solving 2.5 + y = 4.924428901 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 = 4.924428901 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + y = 4.924428901 + -2.5 y = 4.924428901 + -2.5 Combine like terms: 4.924428901 + -2.5 = 2.424428901 y = 2.424428901 Simplifying y = 2.424428901Subproblem 2
y + 2.5 = -4.924428901 Simplifying y + 2.5 = -4.924428901 Reorder the terms: 2.5 + y = -4.924428901 Solving 2.5 + y = -4.924428901 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 = -4.924428901 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + y = -4.924428901 + -2.5 y = -4.924428901 + -2.5 Combine like terms: -4.924428901 + -2.5 = -7.424428901 y = -7.424428901 Simplifying y = -7.424428901Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.424428901, -7.424428901}
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