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Simplifying 2y2 + 8y + 10 = y2 + 1 Reorder the terms: 10 + 8y + 2y2 = y2 + 1 Reorder the terms: 10 + 8y + 2y2 = 1 + y2 Solving 10 + 8y + 2y2 = 1 + y2 Solving for variable 'y'. Reorder the terms: 10 + -1 + 8y + 2y2 + -1y2 = 1 + y2 + -1 + -1y2 Combine like terms: 10 + -1 = 9 9 + 8y + 2y2 + -1y2 = 1 + y2 + -1 + -1y2 Combine like terms: 2y2 + -1y2 = 1y2 9 + 8y + 1y2 = 1 + y2 + -1 + -1y2 Reorder the terms: 9 + 8y + 1y2 = 1 + -1 + y2 + -1y2 Combine like terms: 1 + -1 = 0 9 + 8y + 1y2 = 0 + y2 + -1y2 9 + 8y + 1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 9 + 8y + 1y2 = 0 Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + 8y + -9 + y2 = 0 + -9 Reorder the terms: 9 + -9 + 8y + y2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 8y + y2 = 0 + -9 8y + y2 = 0 + -9 Combine like terms: 0 + -9 = -9 8y + y2 = -9 The y term is 8y. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8y + 16 + y2 = -9 + 16 Reorder the terms: 16 + 8y + y2 = -9 + 16 Combine like terms: -9 + 16 = 7 16 + 8y + y2 = 7 Factor a perfect square on the left side: (y + 4)(y + 4) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (y + 4) equal to 2.645751311 and -2.645751311.Subproblem 1
y + 4 = 2.645751311 Simplifying y + 4 = 2.645751311 Reorder the terms: 4 + y = 2.645751311 Solving 4 + y = 2.645751311 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + y = 2.645751311 + -4 Combine like terms: 4 + -4 = 0 0 + y = 2.645751311 + -4 y = 2.645751311 + -4 Combine like terms: 2.645751311 + -4 = -1.354248689 y = -1.354248689 Simplifying y = -1.354248689Subproblem 2
y + 4 = -2.645751311 Simplifying y + 4 = -2.645751311 Reorder the terms: 4 + y = -2.645751311 Solving 4 + y = -2.645751311 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + y = -2.645751311 + -4 Combine like terms: 4 + -4 = 0 0 + y = -2.645751311 + -4 y = -2.645751311 + -4 Combine like terms: -2.645751311 + -4 = -6.645751311 y = -6.645751311 Simplifying y = -6.645751311Solution
The solution to the problem is based on the solutions from the subproblems. y = {-1.354248689, -6.645751311}
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