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Simplifying y2 + 9 = 2y2 + 2y + -12 Reorder the terms: 9 + y2 = 2y2 + 2y + -12 Reorder the terms: 9 + y2 = -12 + 2y + 2y2 Solving 9 + y2 = -12 + 2y + 2y2 Solving for variable 'y'. Reorder the terms: 9 + 12 + -2y + y2 + -2y2 = -12 + 2y + 2y2 + 12 + -2y + -2y2 Combine like terms: 9 + 12 = 21 21 + -2y + y2 + -2y2 = -12 + 2y + 2y2 + 12 + -2y + -2y2 Combine like terms: y2 + -2y2 = -1y2 21 + -2y + -1y2 = -12 + 2y + 2y2 + 12 + -2y + -2y2 Reorder the terms: 21 + -2y + -1y2 = -12 + 12 + 2y + -2y + 2y2 + -2y2 Combine like terms: -12 + 12 = 0 21 + -2y + -1y2 = 0 + 2y + -2y + 2y2 + -2y2 21 + -2y + -1y2 = 2y + -2y + 2y2 + -2y2 Combine like terms: 2y + -2y = 0 21 + -2y + -1y2 = 0 + 2y2 + -2y2 21 + -2y + -1y2 = 2y2 + -2y2 Combine like terms: 2y2 + -2y2 = 0 21 + -2y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -21 + 2y + y2 = 0 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 = 3.69041576 y = 3.69041576 Simplifying y = 3.69041576Subproblem 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 = -5.69041576 y = -5.69041576 Simplifying y = -5.69041576Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.69041576, -5.69041576}
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