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Simplifying y2 + -2y = 9 Reorder the terms: -2y + y2 = 9 Solving -2y + y2 = 9 Solving for variable 'y'. Reorder the terms: -9 + -2y + y2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + -2y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + -2y + 9 + y2 = 0 + 9 Reorder the terms: -9 + 9 + -2y + y2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -2y + y2 = 0 + 9 -2y + y2 = 0 + 9 Combine like terms: 0 + 9 = 9 -2y + y2 = 9 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 = 9 + 1 Reorder the terms: 1 + -2y + y2 = 9 + 1 Combine like terms: 9 + 1 = 10 1 + -2y + y2 = 10 Factor a perfect square on the left side: (y + -1)(y + -1) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (y + -1) equal to 3.16227766 and -3.16227766.Subproblem 1
y + -1 = 3.16227766 Simplifying y + -1 = 3.16227766 Reorder the terms: -1 + y = 3.16227766 Solving -1 + y = 3.16227766 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 = 3.16227766 + 1 Combine like terms: -1 + 1 = 0 0 + y = 3.16227766 + 1 y = 3.16227766 + 1 Combine like terms: 3.16227766 + 1 = 4.16227766 y = 4.16227766 Simplifying y = 4.16227766Subproblem 2
y + -1 = -3.16227766 Simplifying y + -1 = -3.16227766 Reorder the terms: -1 + y = -3.16227766 Solving -1 + y = -3.16227766 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 = -3.16227766 + 1 Combine like terms: -1 + 1 = 0 0 + y = -3.16227766 + 1 y = -3.16227766 + 1 Combine like terms: -3.16227766 + 1 = -2.16227766 y = -2.16227766 Simplifying y = -2.16227766Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.16227766, -2.16227766}
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