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Simplifying 2y2 + 4y + -7 = y2 + 1 Reorder the terms: -7 + 4y + 2y2 = y2 + 1 Reorder the terms: -7 + 4y + 2y2 = 1 + y2 Solving -7 + 4y + 2y2 = 1 + y2 Solving for variable 'y'. Reorder the terms: -7 + -1 + 4y + 2y2 + -1y2 = 1 + y2 + -1 + -1y2 Combine like terms: -7 + -1 = -8 -8 + 4y + 2y2 + -1y2 = 1 + y2 + -1 + -1y2 Combine like terms: 2y2 + -1y2 = 1y2 -8 + 4y + 1y2 = 1 + y2 + -1 + -1y2 Reorder the terms: -8 + 4y + 1y2 = 1 + -1 + y2 + -1y2 Combine like terms: 1 + -1 = 0 -8 + 4y + 1y2 = 0 + y2 + -1y2 -8 + 4y + 1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 -8 + 4y + 1y2 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + 4y + 8 + y2 = 0 + 8 Reorder the terms: -8 + 8 + 4y + y2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 4y + y2 = 0 + 8 4y + y2 = 0 + 8 Combine like terms: 0 + 8 = 8 4y + y2 = 8 The y term is 4y. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4y + 4 + y2 = 8 + 4 Reorder the terms: 4 + 4y + y2 = 8 + 4 Combine like terms: 8 + 4 = 12 4 + 4y + y2 = 12 Factor a perfect square on the left side: (y + 2)(y + 2) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (y + 2) equal to 3.464101615 and -3.464101615.Subproblem 1
y + 2 = 3.464101615 Simplifying y + 2 = 3.464101615 Reorder the terms: 2 + y = 3.464101615 Solving 2 + y = 3.464101615 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + y = 3.464101615 + -2 Combine like terms: 2 + -2 = 0 0 + y = 3.464101615 + -2 y = 3.464101615 + -2 Combine like terms: 3.464101615 + -2 = 1.464101615 y = 1.464101615 Simplifying y = 1.464101615Subproblem 2
y + 2 = -3.464101615 Simplifying y + 2 = -3.464101615 Reorder the terms: 2 + y = -3.464101615 Solving 2 + y = -3.464101615 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + y = -3.464101615 + -2 Combine like terms: 2 + -2 = 0 0 + y = -3.464101615 + -2 y = -3.464101615 + -2 Combine like terms: -3.464101615 + -2 = -5.464101615 y = -5.464101615 Simplifying y = -5.464101615Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.464101615, -5.464101615}
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