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Simplifying 64 = y(y) + 42y Multiply y * y 64 = y2 + 42y Reorder the terms: 64 = 42y + y2 Solving 64 = 42y + y2 Solving for variable 'y'. Reorder the terms: 64 + -42y + -1y2 = 42y + -42y + y2 + -1y2 Combine like terms: 42y + -42y = 0 64 + -42y + -1y2 = 0 + y2 + -1y2 64 + -42y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 64 + -42y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -64 + 42y + y2 = 0 Move the constant term to the right: Add '64' to each side of the equation. -64 + 42y + 64 + y2 = 0 + 64 Reorder the terms: -64 + 64 + 42y + y2 = 0 + 64 Combine like terms: -64 + 64 = 0 0 + 42y + y2 = 0 + 64 42y + y2 = 0 + 64 Combine like terms: 0 + 64 = 64 42y + y2 = 64 The y term is 42y. Take half its coefficient (21). Square it (441) and add it to both sides. Add '441' to each side of the equation. 42y + 441 + y2 = 64 + 441 Reorder the terms: 441 + 42y + y2 = 64 + 441 Combine like terms: 64 + 441 = 505 441 + 42y + y2 = 505 Factor a perfect square on the left side: (y + 21)(y + 21) = 505 Calculate the square root of the right side: 22.472205054 Break this problem into two subproblems by setting (y + 21) equal to 22.472205054 and -22.472205054.Subproblem 1
y + 21 = 22.472205054 Simplifying y + 21 = 22.472205054 Reorder the terms: 21 + y = 22.472205054 Solving 21 + y = 22.472205054 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-21' to each side of the equation. 21 + -21 + y = 22.472205054 + -21 Combine like terms: 21 + -21 = 0 0 + y = 22.472205054 + -21 y = 22.472205054 + -21 Combine like terms: 22.472205054 + -21 = 1.472205054 y = 1.472205054 Simplifying y = 1.472205054Subproblem 2
y + 21 = -22.472205054 Simplifying y + 21 = -22.472205054 Reorder the terms: 21 + y = -22.472205054 Solving 21 + y = -22.472205054 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-21' to each side of the equation. 21 + -21 + y = -22.472205054 + -21 Combine like terms: 21 + -21 = 0 0 + y = -22.472205054 + -21 y = -22.472205054 + -21 Combine like terms: -22.472205054 + -21 = -43.472205054 y = -43.472205054 Simplifying y = -43.472205054Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.472205054, -43.472205054}
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