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Simplifying y2 + 3y = 38 Reorder the terms: 3y + y2 = 38 Solving 3y + y2 = 38 Solving for variable 'y'. Reorder the terms: -38 + 3y + y2 = 38 + -38 Combine like terms: 38 + -38 = 0 -38 + 3y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '38' to each side of the equation. -38 + 3y + 38 + y2 = 0 + 38 Reorder the terms: -38 + 38 + 3y + y2 = 0 + 38 Combine like terms: -38 + 38 = 0 0 + 3y + y2 = 0 + 38 3y + y2 = 0 + 38 Combine like terms: 0 + 38 = 38 3y + y2 = 38 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 = 38 + 2.25 Reorder the terms: 2.25 + 3y + y2 = 38 + 2.25 Combine like terms: 38 + 2.25 = 40.25 2.25 + 3y + y2 = 40.25 Factor a perfect square on the left side: (y + 1.5)(y + 1.5) = 40.25 Calculate the square root of the right side: 6.34428877 Break this problem into two subproblems by setting (y + 1.5) equal to 6.34428877 and -6.34428877.Subproblem 1
y + 1.5 = 6.34428877 Simplifying y + 1.5 = 6.34428877 Reorder the terms: 1.5 + y = 6.34428877 Solving 1.5 + y = 6.34428877 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 = 6.34428877 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + y = 6.34428877 + -1.5 y = 6.34428877 + -1.5 Combine like terms: 6.34428877 + -1.5 = 4.84428877 y = 4.84428877 Simplifying y = 4.84428877Subproblem 2
y + 1.5 = -6.34428877 Simplifying y + 1.5 = -6.34428877 Reorder the terms: 1.5 + y = -6.34428877 Solving 1.5 + y = -6.34428877 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 = -6.34428877 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + y = -6.34428877 + -1.5 y = -6.34428877 + -1.5 Combine like terms: -6.34428877 + -1.5 = -7.84428877 y = -7.84428877 Simplifying y = -7.84428877Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.84428877, -7.84428877}
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