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Simplifying 2y2 + 20y + -15 = 0 Reorder the terms: -15 + 20y + 2y2 = 0 Solving -15 + 20y + 2y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -7.5 + 10y + y2 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + 10y + 7.5 + y2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + 10y + y2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + 10y + y2 = 0 + 7.5 10y + y2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 10y + y2 = 7.5 The y term is 10y. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10y + 25 + y2 = 7.5 + 25 Reorder the terms: 25 + 10y + y2 = 7.5 + 25 Combine like terms: 7.5 + 25 = 32.5 25 + 10y + y2 = 32.5 Factor a perfect square on the left side: (y + 5)(y + 5) = 32.5 Calculate the square root of the right side: 5.700877125 Break this problem into two subproblems by setting (y + 5) equal to 5.700877125 and -5.700877125.Subproblem 1
y + 5 = 5.700877125 Simplifying y + 5 = 5.700877125 Reorder the terms: 5 + y = 5.700877125 Solving 5 + y = 5.700877125 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + y = 5.700877125 + -5 Combine like terms: 5 + -5 = 0 0 + y = 5.700877125 + -5 y = 5.700877125 + -5 Combine like terms: 5.700877125 + -5 = 0.700877125 y = 0.700877125 Simplifying y = 0.700877125Subproblem 2
y + 5 = -5.700877125 Simplifying y + 5 = -5.700877125 Reorder the terms: 5 + y = -5.700877125 Solving 5 + y = -5.700877125 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + y = -5.700877125 + -5 Combine like terms: 5 + -5 = 0 0 + y = -5.700877125 + -5 y = -5.700877125 + -5 Combine like terms: -5.700877125 + -5 = -10.700877125 y = -10.700877125 Simplifying y = -10.700877125Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.700877125, -10.700877125}
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