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Simplifying 72y2 + 9y + -8 = 0 Reorder the terms: -8 + 9y + 72y2 = 0 Solving -8 + 9y + 72y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 72 the coefficient of the squared term: Divide each side by '72'. -0.1111111111 + 0.125y + y2 = 0 Move the constant term to the right: Add '0.1111111111' to each side of the equation. -0.1111111111 + 0.125y + 0.1111111111 + y2 = 0 + 0.1111111111 Reorder the terms: -0.1111111111 + 0.1111111111 + 0.125y + y2 = 0 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + 0.125y + y2 = 0 + 0.1111111111 0.125y + y2 = 0 + 0.1111111111 Combine like terms: 0 + 0.1111111111 = 0.1111111111 0.125y + y2 = 0.1111111111 The y term is 0.125y. Take half its coefficient (0.0625). Square it (0.00390625) and add it to both sides. Add '0.00390625' to each side of the equation. 0.125y + 0.00390625 + y2 = 0.1111111111 + 0.00390625 Reorder the terms: 0.00390625 + 0.125y + y2 = 0.1111111111 + 0.00390625 Combine like terms: 0.1111111111 + 0.00390625 = 0.1150173611 0.00390625 + 0.125y + y2 = 0.1150173611 Factor a perfect square on the left side: (y + 0.0625)(y + 0.0625) = 0.1150173611 Calculate the square root of the right side: 0.339142096 Break this problem into two subproblems by setting (y + 0.0625) equal to 0.339142096 and -0.339142096.Subproblem 1
y + 0.0625 = 0.339142096 Simplifying y + 0.0625 = 0.339142096 Reorder the terms: 0.0625 + y = 0.339142096 Solving 0.0625 + y = 0.339142096 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.0625' to each side of the equation. 0.0625 + -0.0625 + y = 0.339142096 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + y = 0.339142096 + -0.0625 y = 0.339142096 + -0.0625 Combine like terms: 0.339142096 + -0.0625 = 0.276642096 y = 0.276642096 Simplifying y = 0.276642096Subproblem 2
y + 0.0625 = -0.339142096 Simplifying y + 0.0625 = -0.339142096 Reorder the terms: 0.0625 + y = -0.339142096 Solving 0.0625 + y = -0.339142096 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.0625' to each side of the equation. 0.0625 + -0.0625 + y = -0.339142096 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + y = -0.339142096 + -0.0625 y = -0.339142096 + -0.0625 Combine like terms: -0.339142096 + -0.0625 = -0.401642096 y = -0.401642096 Simplifying y = -0.401642096Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.276642096, -0.401642096}
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