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Simplifying 36 = 25 + 49 + -14y + y2 Combine like terms: 25 + 49 = 74 36 = 74 + -14y + y2 Solving 36 = 74 + -14y + y2 Solving for variable 'y'. Combine like terms: 36 + -74 = -38 -38 + 14y + -1y2 = 74 + -14y + y2 + -74 + 14y + -1y2 Reorder the terms: -38 + 14y + -1y2 = 74 + -74 + -14y + 14y + y2 + -1y2 Combine like terms: 74 + -74 = 0 -38 + 14y + -1y2 = 0 + -14y + 14y + y2 + -1y2 -38 + 14y + -1y2 = -14y + 14y + y2 + -1y2 Combine like terms: -14y + 14y = 0 -38 + 14y + -1y2 = 0 + y2 + -1y2 -38 + 14y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 -38 + 14y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 38 + -14y + y2 = 0 Move the constant term to the right: Add '-38' to each side of the equation. 38 + -14y + -38 + y2 = 0 + -38 Reorder the terms: 38 + -38 + -14y + y2 = 0 + -38 Combine like terms: 38 + -38 = 0 0 + -14y + y2 = 0 + -38 -14y + y2 = 0 + -38 Combine like terms: 0 + -38 = -38 -14y + y2 = -38 The y term is -14y. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14y + 49 + y2 = -38 + 49 Reorder the terms: 49 + -14y + y2 = -38 + 49 Combine like terms: -38 + 49 = 11 49 + -14y + y2 = 11 Factor a perfect square on the left side: (y + -7)(y + -7) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (y + -7) equal to 3.31662479 and -3.31662479.Subproblem 1
y + -7 = 3.31662479 Simplifying y + -7 = 3.31662479 Reorder the terms: -7 + y = 3.31662479 Solving -7 + y = 3.31662479 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + y = 3.31662479 + 7 Combine like terms: -7 + 7 = 0 0 + y = 3.31662479 + 7 y = 3.31662479 + 7 Combine like terms: 3.31662479 + 7 = 10.31662479 y = 10.31662479 Simplifying y = 10.31662479Subproblem 2
y + -7 = -3.31662479 Simplifying y + -7 = -3.31662479 Reorder the terms: -7 + y = -3.31662479 Solving -7 + y = -3.31662479 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + y = -3.31662479 + 7 Combine like terms: -7 + 7 = 0 0 + y = -3.31662479 + 7 y = -3.31662479 + 7 Combine like terms: -3.31662479 + 7 = 3.68337521 y = 3.68337521 Simplifying y = 3.68337521Solution
The solution to the problem is based on the solutions from the subproblems. y = {10.31662479, 3.68337521}
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