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Simplifying 2y2 + -13y + 12 = 0 Reorder the terms: 12 + -13y + 2y2 = 0 Solving 12 + -13y + 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'. 6 + -6.5y + y2 = 0 Move the constant term to the right: Add '-6' to each side of the equation. 6 + -6.5y + -6 + y2 = 0 + -6 Reorder the terms: 6 + -6 + -6.5y + y2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -6.5y + y2 = 0 + -6 -6.5y + y2 = 0 + -6 Combine like terms: 0 + -6 = -6 -6.5y + y2 = -6 The y term is -6.5y. Take half its coefficient (-3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. -6.5y + 10.5625 + y2 = -6 + 10.5625 Reorder the terms: 10.5625 + -6.5y + y2 = -6 + 10.5625 Combine like terms: -6 + 10.5625 = 4.5625 10.5625 + -6.5y + y2 = 4.5625 Factor a perfect square on the left side: (y + -3.25)(y + -3.25) = 4.5625 Calculate the square root of the right side: 2.136000936 Break this problem into two subproblems by setting (y + -3.25) equal to 2.136000936 and -2.136000936.Subproblem 1
y + -3.25 = 2.136000936 Simplifying y + -3.25 = 2.136000936 Reorder the terms: -3.25 + y = 2.136000936 Solving -3.25 + y = 2.136000936 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + y = 2.136000936 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + y = 2.136000936 + 3.25 y = 2.136000936 + 3.25 Combine like terms: 2.136000936 + 3.25 = 5.386000936 y = 5.386000936 Simplifying y = 5.386000936Subproblem 2
y + -3.25 = -2.136000936 Simplifying y + -3.25 = -2.136000936 Reorder the terms: -3.25 + y = -2.136000936 Solving -3.25 + y = -2.136000936 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + y = -2.136000936 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + y = -2.136000936 + 3.25 y = -2.136000936 + 3.25 Combine like terms: -2.136000936 + 3.25 = 1.113999064 y = 1.113999064 Simplifying y = 1.113999064Solution
The solution to the problem is based on the solutions from the subproblems. y = {5.386000936, 1.113999064}
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