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Simplifying y2 + -2y + -40 = 0 Reorder the terms: -40 + -2y + y2 = 0 Solving -40 + -2y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '40' to each side of the equation. -40 + -2y + 40 + y2 = 0 + 40 Reorder the terms: -40 + 40 + -2y + y2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + -2y + y2 = 0 + 40 -2y + y2 = 0 + 40 Combine like terms: 0 + 40 = 40 -2y + y2 = 40 The y term is -2y. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2y + 1 + y2 = 40 + 1 Reorder the terms: 1 + -2y + y2 = 40 + 1 Combine like terms: 40 + 1 = 41 1 + -2y + y2 = 41 Factor a perfect square on the left side: (y + -1)(y + -1) = 41 Calculate the square root of the right side: 6.403124237 Break this problem into two subproblems by setting (y + -1) equal to 6.403124237 and -6.403124237.Subproblem 1
y + -1 = 6.403124237 Simplifying y + -1 = 6.403124237 Reorder the terms: -1 + y = 6.403124237 Solving -1 + y = 6.403124237 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + y = 6.403124237 + 1 Combine like terms: -1 + 1 = 0 0 + y = 6.403124237 + 1 y = 6.403124237 + 1 Combine like terms: 6.403124237 + 1 = 7.403124237 y = 7.403124237 Simplifying y = 7.403124237Subproblem 2
y + -1 = -6.403124237 Simplifying y + -1 = -6.403124237 Reorder the terms: -1 + y = -6.403124237 Solving -1 + y = -6.403124237 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + y = -6.403124237 + 1 Combine like terms: -1 + 1 = 0 0 + y = -6.403124237 + 1 y = -6.403124237 + 1 Combine like terms: -6.403124237 + 1 = -5.403124237 y = -5.403124237 Simplifying y = -5.403124237Solution
The solution to the problem is based on the solutions from the subproblems. y = {7.403124237, -5.403124237}
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