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Simplifying -1y2 + 60y + -200 = 0 Reorder the terms: -200 + 60y + -1y2 = 0 Solving -200 + 60y + -1y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 200 + -60y + y2 = 0 Move the constant term to the right: Add '-200' to each side of the equation. 200 + -60y + -200 + y2 = 0 + -200 Reorder the terms: 200 + -200 + -60y + y2 = 0 + -200 Combine like terms: 200 + -200 = 0 0 + -60y + y2 = 0 + -200 -60y + y2 = 0 + -200 Combine like terms: 0 + -200 = -200 -60y + y2 = -200 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 = -200 + 900 Reorder the terms: 900 + -60y + y2 = -200 + 900 Combine like terms: -200 + 900 = 700 900 + -60y + y2 = 700 Factor a perfect square on the left side: (y + -30)(y + -30) = 700 Calculate the square root of the right side: 26.457513111 Break this problem into two subproblems by setting (y + -30) equal to 26.457513111 and -26.457513111.Subproblem 1
y + -30 = 26.457513111 Simplifying y + -30 = 26.457513111 Reorder the terms: -30 + y = 26.457513111 Solving -30 + y = 26.457513111 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 = 26.457513111 + 30 Combine like terms: -30 + 30 = 0 0 + y = 26.457513111 + 30 y = 26.457513111 + 30 Combine like terms: 26.457513111 + 30 = 56.457513111 y = 56.457513111 Simplifying y = 56.457513111Subproblem 2
y + -30 = -26.457513111 Simplifying y + -30 = -26.457513111 Reorder the terms: -30 + y = -26.457513111 Solving -30 + y = -26.457513111 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 = -26.457513111 + 30 Combine like terms: -30 + 30 = 0 0 + y = -26.457513111 + 30 y = -26.457513111 + 30 Combine like terms: -26.457513111 + 30 = 3.542486889 y = 3.542486889 Simplifying y = 3.542486889Solution
The solution to the problem is based on the solutions from the subproblems. y = {56.457513111, 3.542486889}
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