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Simplifying 3y2 + 31y = 36 Reorder the terms: 31y + 3y2 = 36 Solving 31y + 3y2 = 36 Solving for variable 'y'. Reorder the terms: -36 + 31y + 3y2 = 36 + -36 Combine like terms: 36 + -36 = 0 -36 + 31y + 3y2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -12 + 10.33333333y + y2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + 10.33333333y + 12 + y2 = 0 + 12 Reorder the terms: -12 + 12 + 10.33333333y + y2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 10.33333333y + y2 = 0 + 12 10.33333333y + y2 = 0 + 12 Combine like terms: 0 + 12 = 12 10.33333333y + y2 = 12 The y term is 10.33333333y. Take half its coefficient (5.166666665). Square it (26.69444443) and add it to both sides. Add '26.69444443' to each side of the equation. 10.33333333y + 26.69444443 + y2 = 12 + 26.69444443 Reorder the terms: 26.69444443 + 10.33333333y + y2 = 12 + 26.69444443 Combine like terms: 12 + 26.69444443 = 38.69444443 26.69444443 + 10.33333333y + y2 = 38.69444443 Factor a perfect square on the left side: (y + 5.166666665)(y + 5.166666665) = 38.69444443 Calculate the square root of the right side: 6.220485868 Break this problem into two subproblems by setting (y + 5.166666665) equal to 6.220485868 and -6.220485868.Subproblem 1
y + 5.166666665 = 6.220485868 Simplifying y + 5.166666665 = 6.220485868 Reorder the terms: 5.166666665 + y = 6.220485868 Solving 5.166666665 + y = 6.220485868 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-5.166666665' to each side of the equation. 5.166666665 + -5.166666665 + y = 6.220485868 + -5.166666665 Combine like terms: 5.166666665 + -5.166666665 = 0.000000000 0.000000000 + y = 6.220485868 + -5.166666665 y = 6.220485868 + -5.166666665 Combine like terms: 6.220485868 + -5.166666665 = 1.053819203 y = 1.053819203 Simplifying y = 1.053819203Subproblem 2
y + 5.166666665 = -6.220485868 Simplifying y + 5.166666665 = -6.220485868 Reorder the terms: 5.166666665 + y = -6.220485868 Solving 5.166666665 + y = -6.220485868 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-5.166666665' to each side of the equation. 5.166666665 + -5.166666665 + y = -6.220485868 + -5.166666665 Combine like terms: 5.166666665 + -5.166666665 = 0.000000000 0.000000000 + y = -6.220485868 + -5.166666665 y = -6.220485868 + -5.166666665 Combine like terms: -6.220485868 + -5.166666665 = -11.387152533 y = -11.387152533 Simplifying y = -11.387152533Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.053819203, -11.387152533}
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