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Simplifying 2y2 + -11y + 6 = 0 Reorder the terms: 6 + -11y + 2y2 = 0 Solving 6 + -11y + 2y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 3 + -5.5y + y2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + -5.5y + -3 + y2 = 0 + -3 Reorder the terms: 3 + -3 + -5.5y + y2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5.5y + y2 = 0 + -3 -5.5y + y2 = 0 + -3 Combine like terms: 0 + -3 = -3 -5.5y + y2 = -3 The y term is -5.5y. Take half its coefficient (-2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. -5.5y + 7.5625 + y2 = -3 + 7.5625 Reorder the terms: 7.5625 + -5.5y + y2 = -3 + 7.5625 Combine like terms: -3 + 7.5625 = 4.5625 7.5625 + -5.5y + y2 = 4.5625 Factor a perfect square on the left side: (y + -2.75)(y + -2.75) = 4.5625 Calculate the square root of the right side: 2.136000936 Break this problem into two subproblems by setting (y + -2.75) equal to 2.136000936 and -2.136000936.Subproblem 1
y + -2.75 = 2.136000936 Simplifying y + -2.75 = 2.136000936 Reorder the terms: -2.75 + y = 2.136000936 Solving -2.75 + y = 2.136000936 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + y = 2.136000936 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + y = 2.136000936 + 2.75 y = 2.136000936 + 2.75 Combine like terms: 2.136000936 + 2.75 = 4.886000936 y = 4.886000936 Simplifying y = 4.886000936Subproblem 2
y + -2.75 = -2.136000936 Simplifying y + -2.75 = -2.136000936 Reorder the terms: -2.75 + y = -2.136000936 Solving -2.75 + y = -2.136000936 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + y = -2.136000936 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + y = -2.136000936 + 2.75 y = -2.136000936 + 2.75 Combine like terms: -2.136000936 + 2.75 = 0.613999064 y = 0.613999064 Simplifying y = 0.613999064Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.886000936, 0.613999064}
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