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Simplifying 8y2 + 7y + -5 = 0 Reorder the terms: -5 + 7y + 8y2 = 0 Solving -5 + 7y + 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'. -0.625 + 0.875y + y2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + 0.875y + 0.625 + y2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + 0.875y + y2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + 0.875y + y2 = 0 + 0.625 0.875y + y2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 0.875y + y2 = 0.625 The y term is 0.875y. Take half its coefficient (0.4375). Square it (0.19140625) and add it to both sides. Add '0.19140625' to each side of the equation. 0.875y + 0.19140625 + y2 = 0.625 + 0.19140625 Reorder the terms: 0.19140625 + 0.875y + y2 = 0.625 + 0.19140625 Combine like terms: 0.625 + 0.19140625 = 0.81640625 0.19140625 + 0.875y + y2 = 0.81640625 Factor a perfect square on the left side: (y + 0.4375)(y + 0.4375) = 0.81640625 Calculate the square root of the right side: 0.903552018 Break this problem into two subproblems by setting (y + 0.4375) equal to 0.903552018 and -0.903552018.Subproblem 1
y + 0.4375 = 0.903552018 Simplifying y + 0.4375 = 0.903552018 Reorder the terms: 0.4375 + y = 0.903552018 Solving 0.4375 + y = 0.903552018 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.4375' to each side of the equation. 0.4375 + -0.4375 + y = 0.903552018 + -0.4375 Combine like terms: 0.4375 + -0.4375 = 0.0000 0.0000 + y = 0.903552018 + -0.4375 y = 0.903552018 + -0.4375 Combine like terms: 0.903552018 + -0.4375 = 0.466052018 y = 0.466052018 Simplifying y = 0.466052018Subproblem 2
y + 0.4375 = -0.903552018 Simplifying y + 0.4375 = -0.903552018 Reorder the terms: 0.4375 + y = -0.903552018 Solving 0.4375 + y = -0.903552018 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.4375' to each side of the equation. 0.4375 + -0.4375 + y = -0.903552018 + -0.4375 Combine like terms: 0.4375 + -0.4375 = 0.0000 0.0000 + y = -0.903552018 + -0.4375 y = -0.903552018 + -0.4375 Combine like terms: -0.903552018 + -0.4375 = -1.341052018 y = -1.341052018 Simplifying y = -1.341052018Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.466052018, -1.341052018}
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