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Simplifying 8y2 + -20y + 9 = 0 Reorder the terms: 9 + -20y + 8y2 = 0 Solving 9 + -20y + 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'. 1.125 + -2.5y + y2 = 0 Move the constant term to the right: Add '-1.125' to each side of the equation. 1.125 + -2.5y + -1.125 + y2 = 0 + -1.125 Reorder the terms: 1.125 + -1.125 + -2.5y + y2 = 0 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + -2.5y + y2 = 0 + -1.125 -2.5y + y2 = 0 + -1.125 Combine like terms: 0 + -1.125 = -1.125 -2.5y + y2 = -1.125 The y term is -2.5y. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5y + 1.5625 + y2 = -1.125 + 1.5625 Reorder the terms: 1.5625 + -2.5y + y2 = -1.125 + 1.5625 Combine like terms: -1.125 + 1.5625 = 0.4375 1.5625 + -2.5y + y2 = 0.4375 Factor a perfect square on the left side: (y + -1.25)(y + -1.25) = 0.4375 Calculate the square root of the right side: 0.661437828 Break this problem into two subproblems by setting (y + -1.25) equal to 0.661437828 and -0.661437828.Subproblem 1
y + -1.25 = 0.661437828 Simplifying y + -1.25 = 0.661437828 Reorder the terms: -1.25 + y = 0.661437828 Solving -1.25 + y = 0.661437828 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + y = 0.661437828 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + y = 0.661437828 + 1.25 y = 0.661437828 + 1.25 Combine like terms: 0.661437828 + 1.25 = 1.911437828 y = 1.911437828 Simplifying y = 1.911437828Subproblem 2
y + -1.25 = -0.661437828 Simplifying y + -1.25 = -0.661437828 Reorder the terms: -1.25 + y = -0.661437828 Solving -1.25 + y = -0.661437828 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + y = -0.661437828 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + y = -0.661437828 + 1.25 y = -0.661437828 + 1.25 Combine like terms: -0.661437828 + 1.25 = 0.588562172 y = 0.588562172 Simplifying y = 0.588562172Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.911437828, 0.588562172}
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