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Simplifying -9y2 + 54y + -71 = 0 Reorder the terms: -71 + 54y + -9y2 = 0 Solving -71 + 54y + -9y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. 7.888888889 + -6y + y2 = 0 Move the constant term to the right: Add '-7.888888889' to each side of the equation. 7.888888889 + -6y + -7.888888889 + y2 = 0 + -7.888888889 Reorder the terms: 7.888888889 + -7.888888889 + -6y + y2 = 0 + -7.888888889 Combine like terms: 7.888888889 + -7.888888889 = 0.000000000 0.000000000 + -6y + y2 = 0 + -7.888888889 -6y + y2 = 0 + -7.888888889 Combine like terms: 0 + -7.888888889 = -7.888888889 -6y + y2 = -7.888888889 The y term is -6y. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6y + 9 + y2 = -7.888888889 + 9 Reorder the terms: 9 + -6y + y2 = -7.888888889 + 9 Combine like terms: -7.888888889 + 9 = 1.111111111 9 + -6y + y2 = 1.111111111 Factor a perfect square on the left side: (y + -3)(y + -3) = 1.111111111 Calculate the square root of the right side: 1.054092553 Break this problem into two subproblems by setting (y + -3) equal to 1.054092553 and -1.054092553.Subproblem 1
y + -3 = 1.054092553 Simplifying y + -3 = 1.054092553 Reorder the terms: -3 + y = 1.054092553 Solving -3 + y = 1.054092553 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + y = 1.054092553 + 3 Combine like terms: -3 + 3 = 0 0 + y = 1.054092553 + 3 y = 1.054092553 + 3 Combine like terms: 1.054092553 + 3 = 4.054092553 y = 4.054092553 Simplifying y = 4.054092553Subproblem 2
y + -3 = -1.054092553 Simplifying y + -3 = -1.054092553 Reorder the terms: -3 + y = -1.054092553 Solving -3 + y = -1.054092553 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + y = -1.054092553 + 3 Combine like terms: -3 + 3 = 0 0 + y = -1.054092553 + 3 y = -1.054092553 + 3 Combine like terms: -1.054092553 + 3 = 1.945907447 y = 1.945907447 Simplifying y = 1.945907447Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.054092553, 1.945907447}
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