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Simplifying y2 + -10y = (-14) Reorder the terms: -10y + y2 = (-14) -10y + y2 = -14 Solving -10y + y2 = -14 Solving for variable 'y'. Reorder the terms: 14 + -10y + y2 = -14 + 14 Combine like terms: -14 + 14 = 0 14 + -10y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-14' to each side of the equation. 14 + -10y + -14 + y2 = 0 + -14 Reorder the terms: 14 + -14 + -10y + y2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -10y + y2 = 0 + -14 -10y + y2 = 0 + -14 Combine like terms: 0 + -14 = -14 -10y + y2 = -14 The y term is -10y. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10y + 25 + y2 = -14 + 25 Reorder the terms: 25 + -10y + y2 = -14 + 25 Combine like terms: -14 + 25 = 11 25 + -10y + y2 = 11 Factor a perfect square on the left side: (y + -5)(y + -5) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (y + -5) equal to 3.31662479 and -3.31662479.Subproblem 1
y + -5 = 3.31662479 Simplifying y + -5 = 3.31662479 Reorder the terms: -5 + y = 3.31662479 Solving -5 + y = 3.31662479 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + y = 3.31662479 + 5 Combine like terms: -5 + 5 = 0 0 + y = 3.31662479 + 5 y = 3.31662479 + 5 Combine like terms: 3.31662479 + 5 = 8.31662479 y = 8.31662479 Simplifying y = 8.31662479Subproblem 2
y + -5 = -3.31662479 Simplifying y + -5 = -3.31662479 Reorder the terms: -5 + y = -3.31662479 Solving -5 + y = -3.31662479 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + y = -3.31662479 + 5 Combine like terms: -5 + 5 = 0 0 + y = -3.31662479 + 5 y = -3.31662479 + 5 Combine like terms: -3.31662479 + 5 = 1.68337521 y = 1.68337521 Simplifying y = 1.68337521Solution
The solution to the problem is based on the solutions from the subproblems. y = {8.31662479, 1.68337521}
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