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Simplifying y2 + -2y = 21 Reorder the terms: -2y + y2 = 21 Solving -2y + y2 = 21 Solving for variable 'y'. Reorder the terms: -21 + -2y + y2 = 21 + -21 Combine like terms: 21 + -21 = 0 -21 + -2y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '21' to each side of the equation. -21 + -2y + 21 + y2 = 0 + 21 Reorder the terms: -21 + 21 + -2y + y2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + -2y + y2 = 0 + 21 -2y + y2 = 0 + 21 Combine like terms: 0 + 21 = 21 -2y + y2 = 21 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 = 21 + 1 Reorder the terms: 1 + -2y + y2 = 21 + 1 Combine like terms: 21 + 1 = 22 1 + -2y + y2 = 22 Factor a perfect square on the left side: (y + -1)(y + -1) = 22 Calculate the square root of the right side: 4.69041576 Break this problem into two subproblems by setting (y + -1) equal to 4.69041576 and -4.69041576.Subproblem 1
y + -1 = 4.69041576 Simplifying y + -1 = 4.69041576 Reorder the terms: -1 + y = 4.69041576 Solving -1 + y = 4.69041576 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 = 4.69041576 + 1 Combine like terms: -1 + 1 = 0 0 + y = 4.69041576 + 1 y = 4.69041576 + 1 Combine like terms: 4.69041576 + 1 = 5.69041576 y = 5.69041576 Simplifying y = 5.69041576Subproblem 2
y + -1 = -4.69041576 Simplifying y + -1 = -4.69041576 Reorder the terms: -1 + y = -4.69041576 Solving -1 + y = -4.69041576 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 = -4.69041576 + 1 Combine like terms: -1 + 1 = 0 0 + y = -4.69041576 + 1 y = -4.69041576 + 1 Combine like terms: -4.69041576 + 1 = -3.69041576 y = -3.69041576 Simplifying y = -3.69041576Solution
The solution to the problem is based on the solutions from the subproblems. y = {5.69041576, -3.69041576}
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