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Simplifying -1y2 = 4y + -23 Reorder the terms: -1y2 = -23 + 4y Solving -1y2 = -23 + 4y Solving for variable 'y'. Reorder the terms: 23 + -4y + -1y2 = -23 + 4y + 23 + -4y Reorder the terms: 23 + -4y + -1y2 = -23 + 23 + 4y + -4y Combine like terms: -23 + 23 = 0 23 + -4y + -1y2 = 0 + 4y + -4y 23 + -4y + -1y2 = 4y + -4y Combine like terms: 4y + -4y = 0 23 + -4y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -23 + 4y + y2 = 0 Move the constant term to the right: Add '23' to each side of the equation. -23 + 4y + 23 + y2 = 0 + 23 Reorder the terms: -23 + 23 + 4y + y2 = 0 + 23 Combine like terms: -23 + 23 = 0 0 + 4y + y2 = 0 + 23 4y + y2 = 0 + 23 Combine like terms: 0 + 23 = 23 4y + y2 = 23 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 = 23 + 4 Reorder the terms: 4 + 4y + y2 = 23 + 4 Combine like terms: 23 + 4 = 27 4 + 4y + y2 = 27 Factor a perfect square on the left side: (y + 2)(y + 2) = 27 Calculate the square root of the right side: 5.196152423 Break this problem into two subproblems by setting (y + 2) equal to 5.196152423 and -5.196152423.Subproblem 1
y + 2 = 5.196152423 Simplifying y + 2 = 5.196152423 Reorder the terms: 2 + y = 5.196152423 Solving 2 + y = 5.196152423 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 = 5.196152423 + -2 Combine like terms: 2 + -2 = 0 0 + y = 5.196152423 + -2 y = 5.196152423 + -2 Combine like terms: 5.196152423 + -2 = 3.196152423 y = 3.196152423 Simplifying y = 3.196152423Subproblem 2
y + 2 = -5.196152423 Simplifying y + 2 = -5.196152423 Reorder the terms: 2 + y = -5.196152423 Solving 2 + y = -5.196152423 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 = -5.196152423 + -2 Combine like terms: 2 + -2 = 0 0 + y = -5.196152423 + -2 y = -5.196152423 + -2 Combine like terms: -5.196152423 + -2 = -7.196152423 y = -7.196152423 Simplifying y = -7.196152423Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.196152423, -7.196152423}
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