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Simplifying 3y2 + y + -2 = 7 Reorder the terms: -2 + y + 3y2 = 7 Solving -2 + y + 3y2 = 7 Solving for variable 'y'. Reorder the terms: -2 + -7 + y + 3y2 = 7 + -7 Combine like terms: -2 + -7 = -9 -9 + y + 3y2 = 7 + -7 Combine like terms: 7 + -7 = 0 -9 + y + 3y2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -3 + 0.3333333333y + y2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 0.3333333333y + 3 + y2 = 0 + 3 Reorder the terms: -3 + 3 + 0.3333333333y + y2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 0.3333333333y + y2 = 0 + 3 0.3333333333y + y2 = 0 + 3 Combine like terms: 0 + 3 = 3 0.3333333333y + y2 = 3 The y term is y. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.3333333333y + 0.25 + y2 = 3 + 0.25 Reorder the terms: 0.25 + 0.3333333333y + y2 = 3 + 0.25 Combine like terms: 3 + 0.25 = 3.25 0.25 + 0.3333333333y + y2 = 3.25 Factor a perfect square on the left side: (y + 0.5)(y + 0.5) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (y + 0.5) equal to 1.802775638 and -1.802775638.Subproblem 1
y + 0.5 = 1.802775638 Simplifying y + 0.5 = 1.802775638 Reorder the terms: 0.5 + y = 1.802775638 Solving 0.5 + y = 1.802775638 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y = 1.802775638 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = 1.802775638 + -0.5 y = 1.802775638 + -0.5 Combine like terms: 1.802775638 + -0.5 = 1.302775638 y = 1.302775638 Simplifying y = 1.302775638Subproblem 2
y + 0.5 = -1.802775638 Simplifying y + 0.5 = -1.802775638 Reorder the terms: 0.5 + y = -1.802775638 Solving 0.5 + y = -1.802775638 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y = -1.802775638 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = -1.802775638 + -0.5 y = -1.802775638 + -0.5 Combine like terms: -1.802775638 + -0.5 = -2.302775638 y = -2.302775638 Simplifying y = -2.302775638Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.302775638, -2.302775638}
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