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Simplifying y2 + 8y + 16 = y2 + 2y + 1 + y2 + -2y + -1 Reorder the terms: 16 + 8y + y2 = y2 + 2y + 1 + y2 + -2y + -1 Reorder the terms: 16 + 8y + y2 = 1 + -1 + 2y + -2y + y2 + y2 Combine like terms: 1 + -1 = 0 16 + 8y + y2 = 0 + 2y + -2y + y2 + y2 16 + 8y + y2 = 2y + -2y + y2 + y2 Combine like terms: 2y + -2y = 0 16 + 8y + y2 = 0 + y2 + y2 16 + 8y + y2 = y2 + y2 Combine like terms: y2 + y2 = 2y2 16 + 8y + y2 = 2y2 Solving 16 + 8y + y2 = 2y2 Solving for variable 'y'. Combine like terms: y2 + -2y2 = -1y2 16 + 8y + -1y2 = 2y2 + -2y2 Combine like terms: 2y2 + -2y2 = 0 16 + 8y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -16 + -8y + y2 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + -8y + 16 + y2 = 0 + 16 Reorder the terms: -16 + 16 + -8y + y2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -8y + y2 = 0 + 16 -8y + y2 = 0 + 16 Combine like terms: 0 + 16 = 16 -8y + y2 = 16 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 = 16 + 16 Reorder the terms: 16 + -8y + y2 = 16 + 16 Combine like terms: 16 + 16 = 32 16 + -8y + y2 = 32 Factor a perfect square on the left side: (y + -4)(y + -4) = 32 Calculate the square root of the right side: 5.656854249 Break this problem into two subproblems by setting (y + -4) equal to 5.656854249 and -5.656854249.Subproblem 1
y + -4 = 5.656854249 Simplifying y + -4 = 5.656854249 Reorder the terms: -4 + y = 5.656854249 Solving -4 + y = 5.656854249 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 = 5.656854249 + 4 Combine like terms: -4 + 4 = 0 0 + y = 5.656854249 + 4 y = 5.656854249 + 4 Combine like terms: 5.656854249 + 4 = 9.656854249 y = 9.656854249 Simplifying y = 9.656854249Subproblem 2
y + -4 = -5.656854249 Simplifying y + -4 = -5.656854249 Reorder the terms: -4 + y = -5.656854249 Solving -4 + y = -5.656854249 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 = -5.656854249 + 4 Combine like terms: -4 + 4 = 0 0 + y = -5.656854249 + 4 y = -5.656854249 + 4 Combine like terms: -5.656854249 + 4 = -1.656854249 y = -1.656854249 Simplifying y = -1.656854249Solution
The solution to the problem is based on the solutions from the subproblems. y = {9.656854249, -1.656854249}
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