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Simplifying y(y + 60) = 240 Reorder the terms: y(60 + y) = 240 (60 * y + y * y) = 240 (60y + y2) = 240 Solving 60y + y2 = 240 Solving for variable 'y'. Reorder the terms: -240 + 60y + y2 = 240 + -240 Combine like terms: 240 + -240 = 0 -240 + 60y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '240' to each side of the equation. -240 + 60y + 240 + y2 = 0 + 240 Reorder the terms: -240 + 240 + 60y + y2 = 0 + 240 Combine like terms: -240 + 240 = 0 0 + 60y + y2 = 0 + 240 60y + y2 = 0 + 240 Combine like terms: 0 + 240 = 240 60y + y2 = 240 The y term is 60y. Take half its coefficient (30). Square it (900) and add it to both sides. Add '900' to each side of the equation. 60y + 900 + y2 = 240 + 900 Reorder the terms: 900 + 60y + y2 = 240 + 900 Combine like terms: 240 + 900 = 1140 900 + 60y + y2 = 1140 Factor a perfect square on the left side: (y + 30)(y + 30) = 1140 Calculate the square root of the right side: 33.763886032 Break this problem into two subproblems by setting (y + 30) equal to 33.763886032 and -33.763886032.Subproblem 1
y + 30 = 33.763886032 Simplifying y + 30 = 33.763886032 Reorder the terms: 30 + y = 33.763886032 Solving 30 + y = 33.763886032 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + y = 33.763886032 + -30 Combine like terms: 30 + -30 = 0 0 + y = 33.763886032 + -30 y = 33.763886032 + -30 Combine like terms: 33.763886032 + -30 = 3.763886032 y = 3.763886032 Simplifying y = 3.763886032Subproblem 2
y + 30 = -33.763886032 Simplifying y + 30 = -33.763886032 Reorder the terms: 30 + y = -33.763886032 Solving 30 + y = -33.763886032 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + y = -33.763886032 + -30 Combine like terms: 30 + -30 = 0 0 + y = -33.763886032 + -30 y = -33.763886032 + -30 Combine like terms: -33.763886032 + -30 = -63.763886032 y = -63.763886032 Simplifying y = -63.763886032Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.763886032, -63.763886032}
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