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Simplifying y2 + 8.5y = 15 Reorder the terms: 8.5y + y2 = 15 Solving 8.5y + y2 = 15 Solving for variable 'y'. Reorder the terms: -15 + 8.5y + y2 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + 8.5y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + 8.5y + 15 + y2 = 0 + 15 Reorder the terms: -15 + 15 + 8.5y + y2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 8.5y + y2 = 0 + 15 8.5y + y2 = 0 + 15 Combine like terms: 0 + 15 = 15 8.5y + y2 = 15 The y term is 8.5y. Take half its coefficient (4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. 8.5y + 18.0625 + y2 = 15 + 18.0625 Reorder the terms: 18.0625 + 8.5y + y2 = 15 + 18.0625 Combine like terms: 15 + 18.0625 = 33.0625 18.0625 + 8.5y + y2 = 33.0625 Factor a perfect square on the left side: (y + 4.25)(y + 4.25) = 33.0625 Calculate the square root of the right side: 5.75 Break this problem into two subproblems by setting (y + 4.25) equal to 5.75 and -5.75.Subproblem 1
y + 4.25 = 5.75 Simplifying y + 4.25 = 5.75 Reorder the terms: 4.25 + y = 5.75 Solving 4.25 + y = 5.75 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + y = 5.75 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + y = 5.75 + -4.25 y = 5.75 + -4.25 Combine like terms: 5.75 + -4.25 = 1.5 y = 1.5 Simplifying y = 1.5Subproblem 2
y + 4.25 = -5.75 Simplifying y + 4.25 = -5.75 Reorder the terms: 4.25 + y = -5.75 Solving 4.25 + y = -5.75 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + y = -5.75 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + y = -5.75 + -4.25 y = -5.75 + -4.25 Combine like terms: -5.75 + -4.25 = -10 y = -10 Simplifying y = -10Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.5, -10}
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