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Simplifying 0 = y2 + -18y + -53 Reorder the terms: 0 = -53 + -18y + y2 Solving 0 = -53 + -18y + y2 Solving for variable 'y'. Combine like terms: 0 + 53 = 53 53 + 18y + -1y2 = -53 + -18y + y2 + 53 + 18y + -1y2 Reorder the terms: 53 + 18y + -1y2 = -53 + 53 + -18y + 18y + y2 + -1y2 Combine like terms: -53 + 53 = 0 53 + 18y + -1y2 = 0 + -18y + 18y + y2 + -1y2 53 + 18y + -1y2 = -18y + 18y + y2 + -1y2 Combine like terms: -18y + 18y = 0 53 + 18y + -1y2 = 0 + y2 + -1y2 53 + 18y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 53 + 18y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -53 + -18y + y2 = 0 Move the constant term to the right: Add '53' to each side of the equation. -53 + -18y + 53 + y2 = 0 + 53 Reorder the terms: -53 + 53 + -18y + y2 = 0 + 53 Combine like terms: -53 + 53 = 0 0 + -18y + y2 = 0 + 53 -18y + y2 = 0 + 53 Combine like terms: 0 + 53 = 53 -18y + y2 = 53 The y term is -18y. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18y + 81 + y2 = 53 + 81 Reorder the terms: 81 + -18y + y2 = 53 + 81 Combine like terms: 53 + 81 = 134 81 + -18y + y2 = 134 Factor a perfect square on the left side: (y + -9)(y + -9) = 134 Calculate the square root of the right side: 11.575836903 Break this problem into two subproblems by setting (y + -9) equal to 11.575836903 and -11.575836903.Subproblem 1
y + -9 = 11.575836903 Simplifying y + -9 = 11.575836903 Reorder the terms: -9 + y = 11.575836903 Solving -9 + y = 11.575836903 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + y = 11.575836903 + 9 Combine like terms: -9 + 9 = 0 0 + y = 11.575836903 + 9 y = 11.575836903 + 9 Combine like terms: 11.575836903 + 9 = 20.575836903 y = 20.575836903 Simplifying y = 20.575836903Subproblem 2
y + -9 = -11.575836903 Simplifying y + -9 = -11.575836903 Reorder the terms: -9 + y = -11.575836903 Solving -9 + y = -11.575836903 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + y = -11.575836903 + 9 Combine like terms: -9 + 9 = 0 0 + y = -11.575836903 + 9 y = -11.575836903 + 9 Combine like terms: -11.575836903 + 9 = -2.575836903 y = -2.575836903 Simplifying y = -2.575836903Solution
The solution to the problem is based on the solutions from the subproblems. y = {20.575836903, -2.575836903}
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