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Simplifying -8y2 + 2 + -1y = 0 Reorder the terms: 2 + -1y + -8y2 = 0 Solving 2 + -1y + -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'. -0.25 + 0.125y + y2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + 0.125y + 0.25 + y2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + 0.125y + y2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + 0.125y + y2 = 0 + 0.25 0.125y + y2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 0.125y + y2 = 0.25 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 = 0.25 + 0.00390625 Reorder the terms: 0.00390625 + 0.125y + y2 = 0.25 + 0.00390625 Combine like terms: 0.25 + 0.00390625 = 0.25390625 0.00390625 + 0.125y + y2 = 0.25390625 Factor a perfect square on the left side: (y + 0.0625)(y + 0.0625) = 0.25390625 Calculate the square root of the right side: 0.503891109 Break this problem into two subproblems by setting (y + 0.0625) equal to 0.503891109 and -0.503891109.Subproblem 1
y + 0.0625 = 0.503891109 Simplifying y + 0.0625 = 0.503891109 Reorder the terms: 0.0625 + y = 0.503891109 Solving 0.0625 + y = 0.503891109 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 = 0.503891109 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + y = 0.503891109 + -0.0625 y = 0.503891109 + -0.0625 Combine like terms: 0.503891109 + -0.0625 = 0.441391109 y = 0.441391109 Simplifying y = 0.441391109Subproblem 2
y + 0.0625 = -0.503891109 Simplifying y + 0.0625 = -0.503891109 Reorder the terms: 0.0625 + y = -0.503891109 Solving 0.0625 + y = -0.503891109 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 = -0.503891109 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + y = -0.503891109 + -0.0625 y = -0.503891109 + -0.0625 Combine like terms: -0.503891109 + -0.0625 = -0.566391109 y = -0.566391109 Simplifying y = -0.566391109Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.441391109, -0.566391109}
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