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Simplifying 8y2 = 8y + -1 Reorder the terms: 8y2 = -1 + 8y Solving 8y2 = -1 + 8y Solving for variable 'y'. Reorder the terms: 1 + -8y + 8y2 = -1 + 8y + 1 + -8y Reorder the terms: 1 + -8y + 8y2 = -1 + 1 + 8y + -8y Combine like terms: -1 + 1 = 0 1 + -8y + 8y2 = 0 + 8y + -8y 1 + -8y + 8y2 = 8y + -8y Combine like terms: 8y + -8y = 0 1 + -8y + 8y2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.125 + -1y + y2 = 0 Move the constant term to the right: Add '-0.125' to each side of the equation. 0.125 + -1y + -0.125 + y2 = 0 + -0.125 Reorder the terms: 0.125 + -0.125 + -1y + y2 = 0 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + -1y + y2 = 0 + -0.125 -1y + y2 = 0 + -0.125 Combine like terms: 0 + -0.125 = -0.125 -1y + y2 = -0.125 The y term is -1y. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1y + 0.25 + y2 = -0.125 + 0.25 Reorder the terms: 0.25 + -1y + y2 = -0.125 + 0.25 Combine like terms: -0.125 + 0.25 = 0.125 0.25 + -1y + y2 = 0.125 Factor a perfect square on the left side: (y + -0.5)(y + -0.5) = 0.125 Calculate the square root of the right side: 0.353553391 Break this problem into two subproblems by setting (y + -0.5) equal to 0.353553391 and -0.353553391.Subproblem 1
y + -0.5 = 0.353553391 Simplifying y + -0.5 = 0.353553391 Reorder the terms: -0.5 + y = 0.353553391 Solving -0.5 + y = 0.353553391 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + y = 0.353553391 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + y = 0.353553391 + 0.5 y = 0.353553391 + 0.5 Combine like terms: 0.353553391 + 0.5 = 0.853553391 y = 0.853553391 Simplifying y = 0.853553391Subproblem 2
y + -0.5 = -0.353553391 Simplifying y + -0.5 = -0.353553391 Reorder the terms: -0.5 + y = -0.353553391 Solving -0.5 + y = -0.353553391 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + y = -0.353553391 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + y = -0.353553391 + 0.5 y = -0.353553391 + 0.5 Combine like terms: -0.353553391 + 0.5 = 0.146446609 y = 0.146446609 Simplifying y = 0.146446609Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.853553391, 0.146446609}
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