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Simplifying 8y2 + -41y + -594 = 0 Reorder the terms: -594 + -41y + 8y2 = 0 Solving -594 + -41y + 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'. -74.25 + -5.125y + y2 = 0 Move the constant term to the right: Add '74.25' to each side of the equation. -74.25 + -5.125y + 74.25 + y2 = 0 + 74.25 Reorder the terms: -74.25 + 74.25 + -5.125y + y2 = 0 + 74.25 Combine like terms: -74.25 + 74.25 = 0.00 0.00 + -5.125y + y2 = 0 + 74.25 -5.125y + y2 = 0 + 74.25 Combine like terms: 0 + 74.25 = 74.25 -5.125y + y2 = 74.25 The y term is -5.125y. Take half its coefficient (-2.5625). Square it (6.56640625) and add it to both sides. Add '6.56640625' to each side of the equation. -5.125y + 6.56640625 + y2 = 74.25 + 6.56640625 Reorder the terms: 6.56640625 + -5.125y + y2 = 74.25 + 6.56640625 Combine like terms: 74.25 + 6.56640625 = 80.81640625 6.56640625 + -5.125y + y2 = 80.81640625 Factor a perfect square on the left side: (y + -2.5625)(y + -2.5625) = 80.81640625 Calculate the square root of the right side: 8.989794561 Break this problem into two subproblems by setting (y + -2.5625) equal to 8.989794561 and -8.989794561.Subproblem 1
y + -2.5625 = 8.989794561 Simplifying y + -2.5625 = 8.989794561 Reorder the terms: -2.5625 + y = 8.989794561 Solving -2.5625 + y = 8.989794561 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.5625' to each side of the equation. -2.5625 + 2.5625 + y = 8.989794561 + 2.5625 Combine like terms: -2.5625 + 2.5625 = 0.0000 0.0000 + y = 8.989794561 + 2.5625 y = 8.989794561 + 2.5625 Combine like terms: 8.989794561 + 2.5625 = 11.552294561 y = 11.552294561 Simplifying y = 11.552294561Subproblem 2
y + -2.5625 = -8.989794561 Simplifying y + -2.5625 = -8.989794561 Reorder the terms: -2.5625 + y = -8.989794561 Solving -2.5625 + y = -8.989794561 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.5625' to each side of the equation. -2.5625 + 2.5625 + y = -8.989794561 + 2.5625 Combine like terms: -2.5625 + 2.5625 = 0.0000 0.0000 + y = -8.989794561 + 2.5625 y = -8.989794561 + 2.5625 Combine like terms: -8.989794561 + 2.5625 = -6.427294561 y = -6.427294561 Simplifying y = -6.427294561Solution
The solution to the problem is based on the solutions from the subproblems. y = {11.552294561, -6.427294561}
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