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Simplifying (50 + -1y) * y = 10 Reorder the terms for easier multiplication: y(50 + -1y) = 10 (50 * y + -1y * y) = 10 (50y + -1y2) = 10 Solving 50y + -1y2 = 10 Solving for variable 'y'. Reorder the terms: -10 + 50y + -1y2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + 50y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 10 + -50y + y2 = 0 Move the constant term to the right: Add '-10' to each side of the equation. 10 + -50y + -10 + y2 = 0 + -10 Reorder the terms: 10 + -10 + -50y + y2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -50y + y2 = 0 + -10 -50y + y2 = 0 + -10 Combine like terms: 0 + -10 = -10 -50y + y2 = -10 The y term is -50y. Take half its coefficient (-25). Square it (625) and add it to both sides. Add '625' to each side of the equation. -50y + 625 + y2 = -10 + 625 Reorder the terms: 625 + -50y + y2 = -10 + 625 Combine like terms: -10 + 625 = 615 625 + -50y + y2 = 615 Factor a perfect square on the left side: (y + -25)(y + -25) = 615 Calculate the square root of the right side: 24.799193535 Break this problem into two subproblems by setting (y + -25) equal to 24.799193535 and -24.799193535.Subproblem 1
y + -25 = 24.799193535 Simplifying y + -25 = 24.799193535 Reorder the terms: -25 + y = 24.799193535 Solving -25 + y = 24.799193535 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + y = 24.799193535 + 25 Combine like terms: -25 + 25 = 0 0 + y = 24.799193535 + 25 y = 24.799193535 + 25 Combine like terms: 24.799193535 + 25 = 49.799193535 y = 49.799193535 Simplifying y = 49.799193535Subproblem 2
y + -25 = -24.799193535 Simplifying y + -25 = -24.799193535 Reorder the terms: -25 + y = -24.799193535 Solving -25 + y = -24.799193535 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + y = -24.799193535 + 25 Combine like terms: -25 + 25 = 0 0 + y = -24.799193535 + 25 y = -24.799193535 + 25 Combine like terms: -24.799193535 + 25 = 0.200806465 y = 0.200806465 Simplifying y = 0.200806465Solution
The solution to the problem is based on the solutions from the subproblems. y = {49.799193535, 0.200806465}
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