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Simplifying 8 + -17y + 8y2 = 0 Solving 8 + -17y + 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'. 1 + -2.125y + y2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -2.125y + -1 + y2 = 0 + -1 Reorder the terms: 1 + -1 + -2.125y + y2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2.125y + y2 = 0 + -1 -2.125y + y2 = 0 + -1 Combine like terms: 0 + -1 = -1 -2.125y + y2 = -1 The y term is -2.125y. Take half its coefficient (-1.0625). Square it (1.12890625) and add it to both sides. Add '1.12890625' to each side of the equation. -2.125y + 1.12890625 + y2 = -1 + 1.12890625 Reorder the terms: 1.12890625 + -2.125y + y2 = -1 + 1.12890625 Combine like terms: -1 + 1.12890625 = 0.12890625 1.12890625 + -2.125y + y2 = 0.12890625 Factor a perfect square on the left side: (y + -1.0625)(y + -1.0625) = 0.12890625 Calculate the square root of the right side: 0.359035165 Break this problem into two subproblems by setting (y + -1.0625) equal to 0.359035165 and -0.359035165.Subproblem 1
y + -1.0625 = 0.359035165 Simplifying y + -1.0625 = 0.359035165 Reorder the terms: -1.0625 + y = 0.359035165 Solving -1.0625 + y = 0.359035165 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.0625' to each side of the equation. -1.0625 + 1.0625 + y = 0.359035165 + 1.0625 Combine like terms: -1.0625 + 1.0625 = 0.0000 0.0000 + y = 0.359035165 + 1.0625 y = 0.359035165 + 1.0625 Combine like terms: 0.359035165 + 1.0625 = 1.421535165 y = 1.421535165 Simplifying y = 1.421535165Subproblem 2
y + -1.0625 = -0.359035165 Simplifying y + -1.0625 = -0.359035165 Reorder the terms: -1.0625 + y = -0.359035165 Solving -1.0625 + y = -0.359035165 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.0625' to each side of the equation. -1.0625 + 1.0625 + y = -0.359035165 + 1.0625 Combine like terms: -1.0625 + 1.0625 = 0.0000 0.0000 + y = -0.359035165 + 1.0625 y = -0.359035165 + 1.0625 Combine like terms: -0.359035165 + 1.0625 = 0.703464835 y = 0.703464835 Simplifying y = 0.703464835Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.421535165, 0.703464835}
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