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Simplifying y2 + -20y + 50 = 0 Reorder the terms: 50 + -20y + y2 = 0 Solving 50 + -20y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-50' to each side of the equation. 50 + -20y + -50 + y2 = 0 + -50 Reorder the terms: 50 + -50 + -20y + y2 = 0 + -50 Combine like terms: 50 + -50 = 0 0 + -20y + y2 = 0 + -50 -20y + y2 = 0 + -50 Combine like terms: 0 + -50 = -50 -20y + y2 = -50 The y term is -20y. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20y + 100 + y2 = -50 + 100 Reorder the terms: 100 + -20y + y2 = -50 + 100 Combine like terms: -50 + 100 = 50 100 + -20y + y2 = 50 Factor a perfect square on the left side: (y + -10)(y + -10) = 50 Calculate the square root of the right side: 7.071067812 Break this problem into two subproblems by setting (y + -10) equal to 7.071067812 and -7.071067812.Subproblem 1
y + -10 = 7.071067812 Simplifying y + -10 = 7.071067812 Reorder the terms: -10 + y = 7.071067812 Solving -10 + y = 7.071067812 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + y = 7.071067812 + 10 Combine like terms: -10 + 10 = 0 0 + y = 7.071067812 + 10 y = 7.071067812 + 10 Combine like terms: 7.071067812 + 10 = 17.071067812 y = 17.071067812 Simplifying y = 17.071067812Subproblem 2
y + -10 = -7.071067812 Simplifying y + -10 = -7.071067812 Reorder the terms: -10 + y = -7.071067812 Solving -10 + y = -7.071067812 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + y = -7.071067812 + 10 Combine like terms: -10 + 10 = 0 0 + y = -7.071067812 + 10 y = -7.071067812 + 10 Combine like terms: -7.071067812 + 10 = 2.928932188 y = 2.928932188 Simplifying y = 2.928932188Solution
The solution to the problem is based on the solutions from the subproblems. y = {17.071067812, 2.928932188}
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