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Simplifying 9y2 + -160y + 469 = 0 Reorder the terms: 469 + -160y + 9y2 = 0 Solving 469 + -160y + 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'. 52.11111111 + -17.77777778y + y2 = 0 Move the constant term to the right: Add '-52.11111111' to each side of the equation. 52.11111111 + -17.77777778y + -52.11111111 + y2 = 0 + -52.11111111 Reorder the terms: 52.11111111 + -52.11111111 + -17.77777778y + y2 = 0 + -52.11111111 Combine like terms: 52.11111111 + -52.11111111 = 0.00000000 0.00000000 + -17.77777778y + y2 = 0 + -52.11111111 -17.77777778y + y2 = 0 + -52.11111111 Combine like terms: 0 + -52.11111111 = -52.11111111 -17.77777778y + y2 = -52.11111111 The y term is -17.77777778y. Take half its coefficient (-8.88888889). Square it (79.01234570) and add it to both sides. Add '79.01234570' to each side of the equation. -17.77777778y + 79.01234570 + y2 = -52.11111111 + 79.01234570 Reorder the terms: 79.01234570 + -17.77777778y + y2 = -52.11111111 + 79.01234570 Combine like terms: -52.11111111 + 79.01234570 = 26.90123459 79.01234570 + -17.77777778y + y2 = 26.90123459 Factor a perfect square on the left side: (y + -8.88888889)(y + -8.88888889) = 26.90123459 Calculate the square root of the right side: 5.18664001 Break this problem into two subproblems by setting (y + -8.88888889) equal to 5.18664001 and -5.18664001.Subproblem 1
y + -8.88888889 = 5.18664001 Simplifying y + -8.88888889 = 5.18664001 Reorder the terms: -8.88888889 + y = 5.18664001 Solving -8.88888889 + y = 5.18664001 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '8.88888889' to each side of the equation. -8.88888889 + 8.88888889 + y = 5.18664001 + 8.88888889 Combine like terms: -8.88888889 + 8.88888889 = 0.00000000 0.00000000 + y = 5.18664001 + 8.88888889 y = 5.18664001 + 8.88888889 Combine like terms: 5.18664001 + 8.88888889 = 14.0755289 y = 14.0755289 Simplifying y = 14.0755289Subproblem 2
y + -8.88888889 = -5.18664001 Simplifying y + -8.88888889 = -5.18664001 Reorder the terms: -8.88888889 + y = -5.18664001 Solving -8.88888889 + y = -5.18664001 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '8.88888889' to each side of the equation. -8.88888889 + 8.88888889 + y = -5.18664001 + 8.88888889 Combine like terms: -8.88888889 + 8.88888889 = 0.00000000 0.00000000 + y = -5.18664001 + 8.88888889 y = -5.18664001 + 8.88888889 Combine like terms: -5.18664001 + 8.88888889 = 3.70224888 y = 3.70224888 Simplifying y = 3.70224888Solution
The solution to the problem is based on the solutions from the subproblems. y = {14.0755289, 3.70224888}
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