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Simplifying y2 + -20y = 75 Reorder the terms: -20y + y2 = 75 Solving -20y + y2 = 75 Solving for variable 'y'. Reorder the terms: -75 + -20y + y2 = 75 + -75 Combine like terms: 75 + -75 = 0 -75 + -20y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '75' to each side of the equation. -75 + -20y + 75 + y2 = 0 + 75 Reorder the terms: -75 + 75 + -20y + y2 = 0 + 75 Combine like terms: -75 + 75 = 0 0 + -20y + y2 = 0 + 75 -20y + y2 = 0 + 75 Combine like terms: 0 + 75 = 75 -20y + y2 = 75 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 = 75 + 100 Reorder the terms: 100 + -20y + y2 = 75 + 100 Combine like terms: 75 + 100 = 175 100 + -20y + y2 = 175 Factor a perfect square on the left side: (y + -10)(y + -10) = 175 Calculate the square root of the right side: 13.228756555 Break this problem into two subproblems by setting (y + -10) equal to 13.228756555 and -13.228756555.Subproblem 1
y + -10 = 13.228756555 Simplifying y + -10 = 13.228756555 Reorder the terms: -10 + y = 13.228756555 Solving -10 + y = 13.228756555 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 = 13.228756555 + 10 Combine like terms: -10 + 10 = 0 0 + y = 13.228756555 + 10 y = 13.228756555 + 10 Combine like terms: 13.228756555 + 10 = 23.228756555 y = 23.228756555 Simplifying y = 23.228756555Subproblem 2
y + -10 = -13.228756555 Simplifying y + -10 = -13.228756555 Reorder the terms: -10 + y = -13.228756555 Solving -10 + y = -13.228756555 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 = -13.228756555 + 10 Combine like terms: -10 + 10 = 0 0 + y = -13.228756555 + 10 y = -13.228756555 + 10 Combine like terms: -13.228756555 + 10 = -3.228756555 y = -3.228756555 Simplifying y = -3.228756555Solution
The solution to the problem is based on the solutions from the subproblems. y = {23.228756555, -3.228756555}
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