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Simplifying 3y2 + -33y + 70 = 0 Reorder the terms: 70 + -33y + 3y2 = 0 Solving 70 + -33y + 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'. 23.33333333 + -11y + y2 = 0 Move the constant term to the right: Add '-23.33333333' to each side of the equation. 23.33333333 + -11y + -23.33333333 + y2 = 0 + -23.33333333 Reorder the terms: 23.33333333 + -23.33333333 + -11y + y2 = 0 + -23.33333333 Combine like terms: 23.33333333 + -23.33333333 = 0.00000000 0.00000000 + -11y + y2 = 0 + -23.33333333 -11y + y2 = 0 + -23.33333333 Combine like terms: 0 + -23.33333333 = -23.33333333 -11y + y2 = -23.33333333 The y term is -11y. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11y + 30.25 + y2 = -23.33333333 + 30.25 Reorder the terms: 30.25 + -11y + y2 = -23.33333333 + 30.25 Combine like terms: -23.33333333 + 30.25 = 6.91666667 30.25 + -11y + y2 = 6.91666667 Factor a perfect square on the left side: (y + -5.5)(y + -5.5) = 6.91666667 Calculate the square root of the right side: 2.62995564 Break this problem into two subproblems by setting (y + -5.5) equal to 2.62995564 and -2.62995564.Subproblem 1
y + -5.5 = 2.62995564 Simplifying y + -5.5 = 2.62995564 Reorder the terms: -5.5 + y = 2.62995564 Solving -5.5 + y = 2.62995564 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + y = 2.62995564 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + y = 2.62995564 + 5.5 y = 2.62995564 + 5.5 Combine like terms: 2.62995564 + 5.5 = 8.12995564 y = 8.12995564 Simplifying y = 8.12995564Subproblem 2
y + -5.5 = -2.62995564 Simplifying y + -5.5 = -2.62995564 Reorder the terms: -5.5 + y = -2.62995564 Solving -5.5 + y = -2.62995564 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + y = -2.62995564 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + y = -2.62995564 + 5.5 y = -2.62995564 + 5.5 Combine like terms: -2.62995564 + 5.5 = 2.87004436 y = 2.87004436 Simplifying y = 2.87004436Solution
The solution to the problem is based on the solutions from the subproblems. y = {8.12995564, 2.87004436}
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