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Simplifying 9y2 + 41y + -86 = 0 Reorder the terms: -86 + 41y + 9y2 = 0 Solving -86 + 41y + 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'. -9.555555556 + 4.555555556y + y2 = 0 Move the constant term to the right: Add '9.555555556' to each side of the equation. -9.555555556 + 4.555555556y + 9.555555556 + y2 = 0 + 9.555555556 Reorder the terms: -9.555555556 + 9.555555556 + 4.555555556y + y2 = 0 + 9.555555556 Combine like terms: -9.555555556 + 9.555555556 = 0.000000000 0.000000000 + 4.555555556y + y2 = 0 + 9.555555556 4.555555556y + y2 = 0 + 9.555555556 Combine like terms: 0 + 9.555555556 = 9.555555556 4.555555556y + y2 = 9.555555556 The y term is 4.555555556y. Take half its coefficient (2.277777778). Square it (5.188271606) and add it to both sides. Add '5.188271606' to each side of the equation. 4.555555556y + 5.188271606 + y2 = 9.555555556 + 5.188271606 Reorder the terms: 5.188271606 + 4.555555556y + y2 = 9.555555556 + 5.188271606 Combine like terms: 9.555555556 + 5.188271606 = 14.743827162 5.188271606 + 4.555555556y + y2 = 14.743827162 Factor a perfect square on the left side: (y + 2.277777778)(y + 2.277777778) = 14.743827162 Calculate the square root of the right side: 3.839769155 Break this problem into two subproblems by setting (y + 2.277777778) equal to 3.839769155 and -3.839769155.Subproblem 1
y + 2.277777778 = 3.839769155 Simplifying y + 2.277777778 = 3.839769155 Reorder the terms: 2.277777778 + y = 3.839769155 Solving 2.277777778 + y = 3.839769155 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2.277777778' to each side of the equation. 2.277777778 + -2.277777778 + y = 3.839769155 + -2.277777778 Combine like terms: 2.277777778 + -2.277777778 = 0.000000000 0.000000000 + y = 3.839769155 + -2.277777778 y = 3.839769155 + -2.277777778 Combine like terms: 3.839769155 + -2.277777778 = 1.561991377 y = 1.561991377 Simplifying y = 1.561991377Subproblem 2
y + 2.277777778 = -3.839769155 Simplifying y + 2.277777778 = -3.839769155 Reorder the terms: 2.277777778 + y = -3.839769155 Solving 2.277777778 + y = -3.839769155 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2.277777778' to each side of the equation. 2.277777778 + -2.277777778 + y = -3.839769155 + -2.277777778 Combine like terms: 2.277777778 + -2.277777778 = 0.000000000 0.000000000 + y = -3.839769155 + -2.277777778 y = -3.839769155 + -2.277777778 Combine like terms: -3.839769155 + -2.277777778 = -6.117546933 y = -6.117546933 Simplifying y = -6.117546933Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.561991377, -6.117546933}
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