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Simplifying 8y2 + -1y + 102y + 4 = 0 Reorder the terms: 4 + -1y + 102y + 8y2 = 0 Combine like terms: -1y + 102y = 101y 4 + 101y + 8y2 = 0 Solving 4 + 101y + 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 + 12.625y + y2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + 12.625y + -0.5 + y2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + 12.625y + y2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + 12.625y + y2 = 0 + -0.5 12.625y + y2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 12.625y + y2 = -0.5 The y term is 12.625y. Take half its coefficient (6.3125). Square it (39.84765625) and add it to both sides. Add '39.84765625' to each side of the equation. 12.625y + 39.84765625 + y2 = -0.5 + 39.84765625 Reorder the terms: 39.84765625 + 12.625y + y2 = -0.5 + 39.84765625 Combine like terms: -0.5 + 39.84765625 = 39.34765625 39.84765625 + 12.625y + y2 = 39.34765625 Factor a perfect square on the left side: (y + 6.3125)(y + 6.3125) = 39.34765625 Calculate the square root of the right side: 6.272771018 Break this problem into two subproblems by setting (y + 6.3125) equal to 6.272771018 and -6.272771018.Subproblem 1
y + 6.3125 = 6.272771018 Simplifying y + 6.3125 = 6.272771018 Reorder the terms: 6.3125 + y = 6.272771018 Solving 6.3125 + y = 6.272771018 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-6.3125' to each side of the equation. 6.3125 + -6.3125 + y = 6.272771018 + -6.3125 Combine like terms: 6.3125 + -6.3125 = 0.0000 0.0000 + y = 6.272771018 + -6.3125 y = 6.272771018 + -6.3125 Combine like terms: 6.272771018 + -6.3125 = -0.039728982 y = -0.039728982 Simplifying y = -0.039728982Subproblem 2
y + 6.3125 = -6.272771018 Simplifying y + 6.3125 = -6.272771018 Reorder the terms: 6.3125 + y = -6.272771018 Solving 6.3125 + y = -6.272771018 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-6.3125' to each side of the equation. 6.3125 + -6.3125 + y = -6.272771018 + -6.3125 Combine like terms: 6.3125 + -6.3125 = 0.0000 0.0000 + y = -6.272771018 + -6.3125 y = -6.272771018 + -6.3125 Combine like terms: -6.272771018 + -6.3125 = -12.585271018 y = -12.585271018 Simplifying y = -12.585271018Solution
The solution to the problem is based on the solutions from the subproblems. y = {-0.039728982, -12.585271018}
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