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Simplifying 3y2 + -12y + 7 = 0 Reorder the terms: 7 + -12y + 3y2 = 0 Solving 7 + -12y + 3y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 2.333333333 + -4y + y2 = 0 Move the constant term to the right: Add '-2.333333333' to each side of the equation. 2.333333333 + -4y + -2.333333333 + y2 = 0 + -2.333333333 Reorder the terms: 2.333333333 + -2.333333333 + -4y + y2 = 0 + -2.333333333 Combine like terms: 2.333333333 + -2.333333333 = 0.000000000 0.000000000 + -4y + y2 = 0 + -2.333333333 -4y + y2 = 0 + -2.333333333 Combine like terms: 0 + -2.333333333 = -2.333333333 -4y + y2 = -2.333333333 The y term is -4y. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4y + 4 + y2 = -2.333333333 + 4 Reorder the terms: 4 + -4y + y2 = -2.333333333 + 4 Combine like terms: -2.333333333 + 4 = 1.666666667 4 + -4y + y2 = 1.666666667 Factor a perfect square on the left side: (y + -2)(y + -2) = 1.666666667 Calculate the square root of the right side: 1.290994449 Break this problem into two subproblems by setting (y + -2) equal to 1.290994449 and -1.290994449.Subproblem 1
y + -2 = 1.290994449 Simplifying y + -2 = 1.290994449 Reorder the terms: -2 + y = 1.290994449 Solving -2 + y = 1.290994449 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + y = 1.290994449 + 2 Combine like terms: -2 + 2 = 0 0 + y = 1.290994449 + 2 y = 1.290994449 + 2 Combine like terms: 1.290994449 + 2 = 3.290994449 y = 3.290994449 Simplifying y = 3.290994449Subproblem 2
y + -2 = -1.290994449 Simplifying y + -2 = -1.290994449 Reorder the terms: -2 + y = -1.290994449 Solving -2 + y = -1.290994449 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + y = -1.290994449 + 2 Combine like terms: -2 + 2 = 0 0 + y = -1.290994449 + 2 y = -1.290994449 + 2 Combine like terms: -1.290994449 + 2 = 0.709005551 y = 0.709005551 Simplifying y = 0.709005551Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.290994449, 0.709005551}
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