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Simplifying y2 + -2y = 17 Reorder the terms: -2y + y2 = 17 Solving -2y + y2 = 17 Solving for variable 'y'. Reorder the terms: -17 + -2y + y2 = 17 + -17 Combine like terms: 17 + -17 = 0 -17 + -2y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '17' to each side of the equation. -17 + -2y + 17 + y2 = 0 + 17 Reorder the terms: -17 + 17 + -2y + y2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + -2y + y2 = 0 + 17 -2y + y2 = 0 + 17 Combine like terms: 0 + 17 = 17 -2y + y2 = 17 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 = 17 + 1 Reorder the terms: 1 + -2y + y2 = 17 + 1 Combine like terms: 17 + 1 = 18 1 + -2y + y2 = 18 Factor a perfect square on the left side: (y + -1)(y + -1) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (y + -1) equal to 4.242640687 and -4.242640687.Subproblem 1
y + -1 = 4.242640687 Simplifying y + -1 = 4.242640687 Reorder the terms: -1 + y = 4.242640687 Solving -1 + y = 4.242640687 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 = 4.242640687 + 1 Combine like terms: -1 + 1 = 0 0 + y = 4.242640687 + 1 y = 4.242640687 + 1 Combine like terms: 4.242640687 + 1 = 5.242640687 y = 5.242640687 Simplifying y = 5.242640687Subproblem 2
y + -1 = -4.242640687 Simplifying y + -1 = -4.242640687 Reorder the terms: -1 + y = -4.242640687 Solving -1 + y = -4.242640687 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 = -4.242640687 + 1 Combine like terms: -1 + 1 = 0 0 + y = -4.242640687 + 1 y = -4.242640687 + 1 Combine like terms: -4.242640687 + 1 = -3.242640687 y = -3.242640687 Simplifying y = -3.242640687Solution
The solution to the problem is based on the solutions from the subproblems. y = {5.242640687, -3.242640687}
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