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Simplifying y2 + 2.25 = -3y Reorder the terms: 2.25 + y2 = -3y Solving 2.25 + y2 = -3y Solving for variable 'y'. Reorder the terms: 2.25 + 3y + y2 = -3y + 3y Combine like terms: -3y + 3y = 0 2.25 + 3y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-2.25' to each side of the equation. 2.25 + 3y + -2.25 + y2 = 0 + -2.25 Reorder the terms: 2.25 + -2.25 + 3y + y2 = 0 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + 3y + y2 = 0 + -2.25 3y + y2 = 0 + -2.25 Combine like terms: 0 + -2.25 = -2.25 3y + y2 = -2.25 The y term is 3y. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3y + 2.25 + y2 = -2.25 + 2.25 Reorder the terms: 2.25 + 3y + y2 = -2.25 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 2.25 + 3y + y2 = 0.00 Factor a perfect square on the left side: (y + 1.5)(y + 1.5) = 0.00 Calculate the square root of the right side: 0.00 Break this problem into two subproblems by setting (y + 1.5) equal to 0.00 and 0.00.Subproblem 1
y + 1.5 = 0.00 Simplifying y + 1.5 = 0.00 Reorder the terms: 1.5 + y = 0.00 Solving 1.5 + y = 0.00 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + y = 0.00 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + y = 0.00 + -1.5 y = 0.00 + -1.5 Combine like terms: 0.00 + -1.5 = -1.5 y = -1.5 Simplifying y = -1.5Subproblem 2
y + 1.5 = 0.00 Simplifying y + 1.5 = 0.00 Reorder the terms: 1.5 + y = 0.00 Solving 1.5 + y = 0.00 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + y = 0.00 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + y = 0.00 + -1.5 y = 0.00 + -1.5 Combine like terms: 0.00 + -1.5 = -1.5 y = -1.5 Simplifying y = -1.5Solution
The solution to the problem is based on the solutions from the subproblems. y = {-1.5, -1.5}
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