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Simplifying 9y2 + -40y + -69 = 0 Reorder the terms: -69 + -40y + 9y2 = 0 Solving -69 + -40y + 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'. -7.666666667 + -4.444444444y + y2 = 0 Move the constant term to the right: Add '7.666666667' to each side of the equation. -7.666666667 + -4.444444444y + 7.666666667 + y2 = 0 + 7.666666667 Reorder the terms: -7.666666667 + 7.666666667 + -4.444444444y + y2 = 0 + 7.666666667 Combine like terms: -7.666666667 + 7.666666667 = 0.000000000 0.000000000 + -4.444444444y + y2 = 0 + 7.666666667 -4.444444444y + y2 = 0 + 7.666666667 Combine like terms: 0 + 7.666666667 = 7.666666667 -4.444444444y + y2 = 7.666666667 The y term is -4.444444444y. Take half its coefficient (-2.222222222). Square it (4.938271604) and add it to both sides. Add '4.938271604' to each side of the equation. -4.444444444y + 4.938271604 + y2 = 7.666666667 + 4.938271604 Reorder the terms: 4.938271604 + -4.444444444y + y2 = 7.666666667 + 4.938271604 Combine like terms: 7.666666667 + 4.938271604 = 12.604938271 4.938271604 + -4.444444444y + y2 = 12.604938271 Factor a perfect square on the left side: (y + -2.222222222)(y + -2.222222222) = 12.604938271 Calculate the square root of the right side: 3.550343402 Break this problem into two subproblems by setting (y + -2.222222222) equal to 3.550343402 and -3.550343402.Subproblem 1
y + -2.222222222 = 3.550343402 Simplifying y + -2.222222222 = 3.550343402 Reorder the terms: -2.222222222 + y = 3.550343402 Solving -2.222222222 + y = 3.550343402 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.222222222' to each side of the equation. -2.222222222 + 2.222222222 + y = 3.550343402 + 2.222222222 Combine like terms: -2.222222222 + 2.222222222 = 0.000000000 0.000000000 + y = 3.550343402 + 2.222222222 y = 3.550343402 + 2.222222222 Combine like terms: 3.550343402 + 2.222222222 = 5.772565624 y = 5.772565624 Simplifying y = 5.772565624Subproblem 2
y + -2.222222222 = -3.550343402 Simplifying y + -2.222222222 = -3.550343402 Reorder the terms: -2.222222222 + y = -3.550343402 Solving -2.222222222 + y = -3.550343402 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.222222222' to each side of the equation. -2.222222222 + 2.222222222 + y = -3.550343402 + 2.222222222 Combine like terms: -2.222222222 + 2.222222222 = 0.000000000 0.000000000 + y = -3.550343402 + 2.222222222 y = -3.550343402 + 2.222222222 Combine like terms: -3.550343402 + 2.222222222 = -1.32812118 y = -1.32812118 Simplifying y = -1.32812118Solution
The solution to the problem is based on the solutions from the subproblems. y = {5.772565624, -1.32812118}
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