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Simplifying 8y2 + 9y + -4 = 0 Reorder the terms: -4 + 9y + 8y2 = 0 Solving -4 + 9y + 8y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.5 + 1.125y + y2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 1.125y + 0.5 + y2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 1.125y + y2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 1.125y + y2 = 0 + 0.5 1.125y + y2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 1.125y + y2 = 0.5 The y term is 1.125y. Take half its coefficient (0.5625). Square it (0.31640625) and add it to both sides. Add '0.31640625' to each side of the equation. 1.125y + 0.31640625 + y2 = 0.5 + 0.31640625 Reorder the terms: 0.31640625 + 1.125y + y2 = 0.5 + 0.31640625 Combine like terms: 0.5 + 0.31640625 = 0.81640625 0.31640625 + 1.125y + y2 = 0.81640625 Factor a perfect square on the left side: (y + 0.5625)(y + 0.5625) = 0.81640625 Calculate the square root of the right side: 0.903552018 Break this problem into two subproblems by setting (y + 0.5625) equal to 0.903552018 and -0.903552018.Subproblem 1
y + 0.5625 = 0.903552018 Simplifying y + 0.5625 = 0.903552018 Reorder the terms: 0.5625 + y = 0.903552018 Solving 0.5625 + y = 0.903552018 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5625' to each side of the equation. 0.5625 + -0.5625 + y = 0.903552018 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + y = 0.903552018 + -0.5625 y = 0.903552018 + -0.5625 Combine like terms: 0.903552018 + -0.5625 = 0.341052018 y = 0.341052018 Simplifying y = 0.341052018Subproblem 2
y + 0.5625 = -0.903552018 Simplifying y + 0.5625 = -0.903552018 Reorder the terms: 0.5625 + y = -0.903552018 Solving 0.5625 + y = -0.903552018 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5625' to each side of the equation. 0.5625 + -0.5625 + y = -0.903552018 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + y = -0.903552018 + -0.5625 y = -0.903552018 + -0.5625 Combine like terms: -0.903552018 + -0.5625 = -1.466052018 y = -1.466052018 Simplifying y = -1.466052018Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.341052018, -1.466052018}
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