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Simplifying -1y2 = 6y + -23 Reorder the terms: -1y2 = -23 + 6y Solving -1y2 = -23 + 6y Solving for variable 'y'. Reorder the terms: 23 + -6y + -1y2 = -23 + 6y + 23 + -6y Reorder the terms: 23 + -6y + -1y2 = -23 + 23 + 6y + -6y Combine like terms: -23 + 23 = 0 23 + -6y + -1y2 = 0 + 6y + -6y 23 + -6y + -1y2 = 6y + -6y Combine like terms: 6y + -6y = 0 23 + -6y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -23 + 6y + y2 = 0 Move the constant term to the right: Add '23' to each side of the equation. -23 + 6y + 23 + y2 = 0 + 23 Reorder the terms: -23 + 23 + 6y + y2 = 0 + 23 Combine like terms: -23 + 23 = 0 0 + 6y + y2 = 0 + 23 6y + y2 = 0 + 23 Combine like terms: 0 + 23 = 23 6y + y2 = 23 The y term is 6y. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6y + 9 + y2 = 23 + 9 Reorder the terms: 9 + 6y + y2 = 23 + 9 Combine like terms: 23 + 9 = 32 9 + 6y + y2 = 32 Factor a perfect square on the left side: (y + 3)(y + 3) = 32 Calculate the square root of the right side: 5.656854249 Break this problem into two subproblems by setting (y + 3) equal to 5.656854249 and -5.656854249.Subproblem 1
y + 3 = 5.656854249 Simplifying y + 3 = 5.656854249 Reorder the terms: 3 + y = 5.656854249 Solving 3 + y = 5.656854249 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + y = 5.656854249 + -3 Combine like terms: 3 + -3 = 0 0 + y = 5.656854249 + -3 y = 5.656854249 + -3 Combine like terms: 5.656854249 + -3 = 2.656854249 y = 2.656854249 Simplifying y = 2.656854249Subproblem 2
y + 3 = -5.656854249 Simplifying y + 3 = -5.656854249 Reorder the terms: 3 + y = -5.656854249 Solving 3 + y = -5.656854249 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + y = -5.656854249 + -3 Combine like terms: 3 + -3 = 0 0 + y = -5.656854249 + -3 y = -5.656854249 + -3 Combine like terms: -5.656854249 + -3 = -8.656854249 y = -8.656854249 Simplifying y = -8.656854249Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.656854249, -8.656854249}
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