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Simplifying 2y2 + -12y + 7 = 0 Reorder the terms: 7 + -12y + 2y2 = 0 Solving 7 + -12y + 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 + -6y + y2 = 0 Move the constant term to the right: Add '-3.5' to each side of the equation. 3.5 + -6y + -3.5 + y2 = 0 + -3.5 Reorder the terms: 3.5 + -3.5 + -6y + y2 = 0 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + -6y + y2 = 0 + -3.5 -6y + y2 = 0 + -3.5 Combine like terms: 0 + -3.5 = -3.5 -6y + y2 = -3.5 The y term is -6y. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6y + 9 + y2 = -3.5 + 9 Reorder the terms: 9 + -6y + y2 = -3.5 + 9 Combine like terms: -3.5 + 9 = 5.5 9 + -6y + y2 = 5.5 Factor a perfect square on the left side: (y + -3)(y + -3) = 5.5 Calculate the square root of the right side: 2.34520788 Break this problem into two subproblems by setting (y + -3) equal to 2.34520788 and -2.34520788.Subproblem 1
y + -3 = 2.34520788 Simplifying y + -3 = 2.34520788 Reorder the terms: -3 + y = 2.34520788 Solving -3 + y = 2.34520788 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + y = 2.34520788 + 3 Combine like terms: -3 + 3 = 0 0 + y = 2.34520788 + 3 y = 2.34520788 + 3 Combine like terms: 2.34520788 + 3 = 5.34520788 y = 5.34520788 Simplifying y = 5.34520788Subproblem 2
y + -3 = -2.34520788 Simplifying y + -3 = -2.34520788 Reorder the terms: -3 + y = -2.34520788 Solving -3 + y = -2.34520788 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + y = -2.34520788 + 3 Combine like terms: -3 + 3 = 0 0 + y = -2.34520788 + 3 y = -2.34520788 + 3 Combine like terms: -2.34520788 + 3 = 0.65479212 y = 0.65479212 Simplifying y = 0.65479212Solution
The solution to the problem is based on the solutions from the subproblems. y = {5.34520788, 0.65479212}
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