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Simplifying 9y2 + -46y + -400 = 0 Reorder the terms: -400 + -46y + 9y2 = 0 Solving -400 + -46y + 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'. -44.44444444 + -5.111111111y + y2 = 0 Move the constant term to the right: Add '44.44444444' to each side of the equation. -44.44444444 + -5.111111111y + 44.44444444 + y2 = 0 + 44.44444444 Reorder the terms: -44.44444444 + 44.44444444 + -5.111111111y + y2 = 0 + 44.44444444 Combine like terms: -44.44444444 + 44.44444444 = 0.00000000 0.00000000 + -5.111111111y + y2 = 0 + 44.44444444 -5.111111111y + y2 = 0 + 44.44444444 Combine like terms: 0 + 44.44444444 = 44.44444444 -5.111111111y + y2 = 44.44444444 The y term is -5.111111111y. Take half its coefficient (-2.555555556). Square it (6.530864200) and add it to both sides. Add '6.530864200' to each side of the equation. -5.111111111y + 6.530864200 + y2 = 44.44444444 + 6.530864200 Reorder the terms: 6.530864200 + -5.111111111y + y2 = 44.44444444 + 6.530864200 Combine like terms: 44.44444444 + 6.530864200 = 50.97530864 6.530864200 + -5.111111111y + y2 = 50.97530864 Factor a perfect square on the left side: (y + -2.555555556)(y + -2.555555556) = 50.97530864 Calculate the square root of the right side: 7.139699478 Break this problem into two subproblems by setting (y + -2.555555556) equal to 7.139699478 and -7.139699478.Subproblem 1
y + -2.555555556 = 7.139699478 Simplifying y + -2.555555556 = 7.139699478 Reorder the terms: -2.555555556 + y = 7.139699478 Solving -2.555555556 + y = 7.139699478 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.555555556' to each side of the equation. -2.555555556 + 2.555555556 + y = 7.139699478 + 2.555555556 Combine like terms: -2.555555556 + 2.555555556 = 0.000000000 0.000000000 + y = 7.139699478 + 2.555555556 y = 7.139699478 + 2.555555556 Combine like terms: 7.139699478 + 2.555555556 = 9.695255034 y = 9.695255034 Simplifying y = 9.695255034Subproblem 2
y + -2.555555556 = -7.139699478 Simplifying y + -2.555555556 = -7.139699478 Reorder the terms: -2.555555556 + y = -7.139699478 Solving -2.555555556 + y = -7.139699478 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.555555556' to each side of the equation. -2.555555556 + 2.555555556 + y = -7.139699478 + 2.555555556 Combine like terms: -2.555555556 + 2.555555556 = 0.000000000 0.000000000 + y = -7.139699478 + 2.555555556 y = -7.139699478 + 2.555555556 Combine like terms: -7.139699478 + 2.555555556 = -4.584143922 y = -4.584143922 Simplifying y = -4.584143922Solution
The solution to the problem is based on the solutions from the subproblems. y = {9.695255034, -4.584143922}
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