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Simplifying 486 + 36y = 27 + y * y Multiply y * y 486 + 36y = 27 + y2 Solving 486 + 36y = 27 + y2 Solving for variable 'y'. Reorder the terms: 486 + -27 + 36y + -1y2 = 27 + y2 + -27 + -1y2 Combine like terms: 486 + -27 = 459 459 + 36y + -1y2 = 27 + y2 + -27 + -1y2 Reorder the terms: 459 + 36y + -1y2 = 27 + -27 + y2 + -1y2 Combine like terms: 27 + -27 = 0 459 + 36y + -1y2 = 0 + y2 + -1y2 459 + 36y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 459 + 36y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -459 + -36y + y2 = 0 Move the constant term to the right: Add '459' to each side of the equation. -459 + -36y + 459 + y2 = 0 + 459 Reorder the terms: -459 + 459 + -36y + y2 = 0 + 459 Combine like terms: -459 + 459 = 0 0 + -36y + y2 = 0 + 459 -36y + y2 = 0 + 459 Combine like terms: 0 + 459 = 459 -36y + y2 = 459 The y term is -36y. Take half its coefficient (-18). Square it (324) and add it to both sides. Add '324' to each side of the equation. -36y + 324 + y2 = 459 + 324 Reorder the terms: 324 + -36y + y2 = 459 + 324 Combine like terms: 459 + 324 = 783 324 + -36y + y2 = 783 Factor a perfect square on the left side: (y + -18)(y + -18) = 783 Calculate the square root of the right side: 27.982137159 Break this problem into two subproblems by setting (y + -18) equal to 27.982137159 and -27.982137159.Subproblem 1
y + -18 = 27.982137159 Simplifying y + -18 = 27.982137159 Reorder the terms: -18 + y = 27.982137159 Solving -18 + y = 27.982137159 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + y = 27.982137159 + 18 Combine like terms: -18 + 18 = 0 0 + y = 27.982137159 + 18 y = 27.982137159 + 18 Combine like terms: 27.982137159 + 18 = 45.982137159 y = 45.982137159 Simplifying y = 45.982137159Subproblem 2
y + -18 = -27.982137159 Simplifying y + -18 = -27.982137159 Reorder the terms: -18 + y = -27.982137159 Solving -18 + y = -27.982137159 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + y = -27.982137159 + 18 Combine like terms: -18 + 18 = 0 0 + y = -27.982137159 + 18 y = -27.982137159 + 18 Combine like terms: -27.982137159 + 18 = -9.982137159 y = -9.982137159 Simplifying y = -9.982137159Solution
The solution to the problem is based on the solutions from the subproblems. y = {45.982137159, -9.982137159}
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