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Simplifying 0 = y2 + -240y + 11000 Reorder the terms: 0 = 11000 + -240y + y2 Solving 0 = 11000 + -240y + y2 Solving for variable 'y'. Combine like terms: 0 + -11000 = -11000 -11000 + 240y + -1y2 = 11000 + -240y + y2 + -11000 + 240y + -1y2 Reorder the terms: -11000 + 240y + -1y2 = 11000 + -11000 + -240y + 240y + y2 + -1y2 Combine like terms: 11000 + -11000 = 0 -11000 + 240y + -1y2 = 0 + -240y + 240y + y2 + -1y2 -11000 + 240y + -1y2 = -240y + 240y + y2 + -1y2 Combine like terms: -240y + 240y = 0 -11000 + 240y + -1y2 = 0 + y2 + -1y2 -11000 + 240y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 -11000 + 240y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 11000 + -240y + y2 = 0 Move the constant term to the right: Add '-11000' to each side of the equation. 11000 + -240y + -11000 + y2 = 0 + -11000 Reorder the terms: 11000 + -11000 + -240y + y2 = 0 + -11000 Combine like terms: 11000 + -11000 = 0 0 + -240y + y2 = 0 + -11000 -240y + y2 = 0 + -11000 Combine like terms: 0 + -11000 = -11000 -240y + y2 = -11000 The y term is -240y. Take half its coefficient (-120). Square it (14400) and add it to both sides. Add '14400' to each side of the equation. -240y + 14400 + y2 = -11000 + 14400 Reorder the terms: 14400 + -240y + y2 = -11000 + 14400 Combine like terms: -11000 + 14400 = 3400 14400 + -240y + y2 = 3400 Factor a perfect square on the left side: (y + -120)(y + -120) = 3400 Calculate the square root of the right side: 58.309518948 Break this problem into two subproblems by setting (y + -120) equal to 58.309518948 and -58.309518948.Subproblem 1
y + -120 = 58.309518948 Simplifying y + -120 = 58.309518948 Reorder the terms: -120 + y = 58.309518948 Solving -120 + y = 58.309518948 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '120' to each side of the equation. -120 + 120 + y = 58.309518948 + 120 Combine like terms: -120 + 120 = 0 0 + y = 58.309518948 + 120 y = 58.309518948 + 120 Combine like terms: 58.309518948 + 120 = 178.309518948 y = 178.309518948 Simplifying y = 178.309518948Subproblem 2
y + -120 = -58.309518948 Simplifying y + -120 = -58.309518948 Reorder the terms: -120 + y = -58.309518948 Solving -120 + y = -58.309518948 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '120' to each side of the equation. -120 + 120 + y = -58.309518948 + 120 Combine like terms: -120 + 120 = 0 0 + y = -58.309518948 + 120 y = -58.309518948 + 120 Combine like terms: -58.309518948 + 120 = 61.690481052 y = 61.690481052 Simplifying y = 61.690481052Solution
The solution to the problem is based on the solutions from the subproblems. y = {178.309518948, 61.690481052}
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