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Simplifying 2y = y2 + -26 Reorder the terms: 2y = -26 + y2 Solving 2y = -26 + y2 Solving for variable 'y'. Reorder the terms: 26 + 2y + -1y2 = -26 + y2 + 26 + -1y2 Reorder the terms: 26 + 2y + -1y2 = -26 + 26 + y2 + -1y2 Combine like terms: -26 + 26 = 0 26 + 2y + -1y2 = 0 + y2 + -1y2 26 + 2y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 26 + 2y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -26 + -2y + y2 = 0 Move the constant term to the right: Add '26' to each side of the equation. -26 + -2y + 26 + y2 = 0 + 26 Reorder the terms: -26 + 26 + -2y + y2 = 0 + 26 Combine like terms: -26 + 26 = 0 0 + -2y + y2 = 0 + 26 -2y + y2 = 0 + 26 Combine like terms: 0 + 26 = 26 -2y + y2 = 26 The y term is -2y. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2y + 1 + y2 = 26 + 1 Reorder the terms: 1 + -2y + y2 = 26 + 1 Combine like terms: 26 + 1 = 27 1 + -2y + y2 = 27 Factor a perfect square on the left side: (y + -1)(y + -1) = 27 Calculate the square root of the right side: 5.196152423 Break this problem into two subproblems by setting (y + -1) equal to 5.196152423 and -5.196152423.Subproblem 1
y + -1 = 5.196152423 Simplifying y + -1 = 5.196152423 Reorder the terms: -1 + y = 5.196152423 Solving -1 + y = 5.196152423 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + y = 5.196152423 + 1 Combine like terms: -1 + 1 = 0 0 + y = 5.196152423 + 1 y = 5.196152423 + 1 Combine like terms: 5.196152423 + 1 = 6.196152423 y = 6.196152423 Simplifying y = 6.196152423Subproblem 2
y + -1 = -5.196152423 Simplifying y + -1 = -5.196152423 Reorder the terms: -1 + y = -5.196152423 Solving -1 + y = -5.196152423 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + y = -5.196152423 + 1 Combine like terms: -1 + 1 = 0 0 + y = -5.196152423 + 1 y = -5.196152423 + 1 Combine like terms: -5.196152423 + 1 = -4.196152423 y = -4.196152423 Simplifying y = -4.196152423Solution
The solution to the problem is based on the solutions from the subproblems. y = {6.196152423, -4.196152423}
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