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Simplifying 10y + 5 + -1y2 = 25y + -10 Reorder the terms: 5 + 10y + -1y2 = 25y + -10 Reorder the terms: 5 + 10y + -1y2 = -10 + 25y Solving 5 + 10y + -1y2 = -10 + 25y Solving for variable 'y'. Reorder the terms: 5 + 10 + 10y + -25y + -1y2 = -10 + 25y + 10 + -25y Combine like terms: 5 + 10 = 15 15 + 10y + -25y + -1y2 = -10 + 25y + 10 + -25y Combine like terms: 10y + -25y = -15y 15 + -15y + -1y2 = -10 + 25y + 10 + -25y Reorder the terms: 15 + -15y + -1y2 = -10 + 10 + 25y + -25y Combine like terms: -10 + 10 = 0 15 + -15y + -1y2 = 0 + 25y + -25y 15 + -15y + -1y2 = 25y + -25y Combine like terms: 25y + -25y = 0 15 + -15y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -15 + 15y + y2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + 15y + 15 + y2 = 0 + 15 Reorder the terms: -15 + 15 + 15y + y2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 15y + y2 = 0 + 15 15y + y2 = 0 + 15 Combine like terms: 0 + 15 = 15 15y + y2 = 15 The y term is 15y. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15y + 56.25 + y2 = 15 + 56.25 Reorder the terms: 56.25 + 15y + y2 = 15 + 56.25 Combine like terms: 15 + 56.25 = 71.25 56.25 + 15y + y2 = 71.25 Factor a perfect square on the left side: (y + 7.5)(y + 7.5) = 71.25 Calculate the square root of the right side: 8.440971508 Break this problem into two subproblems by setting (y + 7.5) equal to 8.440971508 and -8.440971508.Subproblem 1
y + 7.5 = 8.440971508 Simplifying y + 7.5 = 8.440971508 Reorder the terms: 7.5 + y = 8.440971508 Solving 7.5 + y = 8.440971508 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + y = 8.440971508 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + y = 8.440971508 + -7.5 y = 8.440971508 + -7.5 Combine like terms: 8.440971508 + -7.5 = 0.940971508 y = 0.940971508 Simplifying y = 0.940971508Subproblem 2
y + 7.5 = -8.440971508 Simplifying y + 7.5 = -8.440971508 Reorder the terms: 7.5 + y = -8.440971508 Solving 7.5 + y = -8.440971508 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + y = -8.440971508 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + y = -8.440971508 + -7.5 y = -8.440971508 + -7.5 Combine like terms: -8.440971508 + -7.5 = -15.940971508 y = -15.940971508 Simplifying y = -15.940971508Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.940971508, -15.940971508}
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