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Simplifying 2y2 + 60y + -500 = 0 Reorder the terms: -500 + 60y + 2y2 = 0 Solving -500 + 60y + 2y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(-250 + 30y + y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-250 + 30y + y2)' equal to zero and attempt to solve: Simplifying -250 + 30y + y2 = 0 Solving -250 + 30y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '250' to each side of the equation. -250 + 30y + 250 + y2 = 0 + 250 Reorder the terms: -250 + 250 + 30y + y2 = 0 + 250 Combine like terms: -250 + 250 = 0 0 + 30y + y2 = 0 + 250 30y + y2 = 0 + 250 Combine like terms: 0 + 250 = 250 30y + y2 = 250 The y term is 30y. Take half its coefficient (15). Square it (225) and add it to both sides. Add '225' to each side of the equation. 30y + 225 + y2 = 250 + 225 Reorder the terms: 225 + 30y + y2 = 250 + 225 Combine like terms: 250 + 225 = 475 225 + 30y + y2 = 475 Factor a perfect square on the left side: (y + 15)(y + 15) = 475 Calculate the square root of the right side: 21.794494718 Break this problem into two subproblems by setting (y + 15) equal to 21.794494718 and -21.794494718.Subproblem 1
y + 15 = 21.794494718 Simplifying y + 15 = 21.794494718 Reorder the terms: 15 + y = 21.794494718 Solving 15 + y = 21.794494718 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + y = 21.794494718 + -15 Combine like terms: 15 + -15 = 0 0 + y = 21.794494718 + -15 y = 21.794494718 + -15 Combine like terms: 21.794494718 + -15 = 6.794494718 y = 6.794494718 Simplifying y = 6.794494718Subproblem 2
y + 15 = -21.794494718 Simplifying y + 15 = -21.794494718 Reorder the terms: 15 + y = -21.794494718 Solving 15 + y = -21.794494718 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + y = -21.794494718 + -15 Combine like terms: 15 + -15 = 0 0 + y = -21.794494718 + -15 y = -21.794494718 + -15 Combine like terms: -21.794494718 + -15 = -36.794494718 y = -36.794494718 Simplifying y = -36.794494718Solution
The solution to the problem is based on the solutions from the subproblems. y = {6.794494718, -36.794494718}Solution
y = {6.794494718, -36.794494718}
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