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Simplifying y2 + -36y + 81 = 0 Reorder the terms: 81 + -36y + y2 = 0 Solving 81 + -36y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-81' to each side of the equation. 81 + -36y + -81 + y2 = 0 + -81 Reorder the terms: 81 + -81 + -36y + y2 = 0 + -81 Combine like terms: 81 + -81 = 0 0 + -36y + y2 = 0 + -81 -36y + y2 = 0 + -81 Combine like terms: 0 + -81 = -81 -36y + y2 = -81 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 = -81 + 324 Reorder the terms: 324 + -36y + y2 = -81 + 324 Combine like terms: -81 + 324 = 243 324 + -36y + y2 = 243 Factor a perfect square on the left side: (y + -18)(y + -18) = 243 Calculate the square root of the right side: 15.588457268 Break this problem into two subproblems by setting (y + -18) equal to 15.588457268 and -15.588457268.Subproblem 1
y + -18 = 15.588457268 Simplifying y + -18 = 15.588457268 Reorder the terms: -18 + y = 15.588457268 Solving -18 + y = 15.588457268 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 = 15.588457268 + 18 Combine like terms: -18 + 18 = 0 0 + y = 15.588457268 + 18 y = 15.588457268 + 18 Combine like terms: 15.588457268 + 18 = 33.588457268 y = 33.588457268 Simplifying y = 33.588457268Subproblem 2
y + -18 = -15.588457268 Simplifying y + -18 = -15.588457268 Reorder the terms: -18 + y = -15.588457268 Solving -18 + y = -15.588457268 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 = -15.588457268 + 18 Combine like terms: -18 + 18 = 0 0 + y = -15.588457268 + 18 y = -15.588457268 + 18 Combine like terms: -15.588457268 + 18 = 2.411542732 y = 2.411542732 Simplifying y = 2.411542732Solution
The solution to the problem is based on the solutions from the subproblems. y = {33.588457268, 2.411542732}
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