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Simplifying 64 = 13y + y2 Solving 64 = 13y + y2 Solving for variable 'y'. Reorder the terms: 64 + -13y + -1y2 = 13y + -13y + y2 + -1y2 Combine like terms: 13y + -13y = 0 64 + -13y + -1y2 = 0 + y2 + -1y2 64 + -13y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 64 + -13y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -64 + 13y + y2 = 0 Move the constant term to the right: Add '64' to each side of the equation. -64 + 13y + 64 + y2 = 0 + 64 Reorder the terms: -64 + 64 + 13y + y2 = 0 + 64 Combine like terms: -64 + 64 = 0 0 + 13y + y2 = 0 + 64 13y + y2 = 0 + 64 Combine like terms: 0 + 64 = 64 13y + y2 = 64 The y term is 13y. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13y + 42.25 + y2 = 64 + 42.25 Reorder the terms: 42.25 + 13y + y2 = 64 + 42.25 Combine like terms: 64 + 42.25 = 106.25 42.25 + 13y + y2 = 106.25 Factor a perfect square on the left side: (y + 6.5)(y + 6.5) = 106.25 Calculate the square root of the right side: 10.307764064 Break this problem into two subproblems by setting (y + 6.5) equal to 10.307764064 and -10.307764064.Subproblem 1
y + 6.5 = 10.307764064 Simplifying y + 6.5 = 10.307764064 Reorder the terms: 6.5 + y = 10.307764064 Solving 6.5 + y = 10.307764064 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + y = 10.307764064 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + y = 10.307764064 + -6.5 y = 10.307764064 + -6.5 Combine like terms: 10.307764064 + -6.5 = 3.807764064 y = 3.807764064 Simplifying y = 3.807764064Subproblem 2
y + 6.5 = -10.307764064 Simplifying y + 6.5 = -10.307764064 Reorder the terms: 6.5 + y = -10.307764064 Solving 6.5 + y = -10.307764064 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + y = -10.307764064 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + y = -10.307764064 + -6.5 y = -10.307764064 + -6.5 Combine like terms: -10.307764064 + -6.5 = -16.807764064 y = -16.807764064 Simplifying y = -16.807764064Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.807764064, -16.807764064}
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