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Simplifying 0 = y2 + -11y + 14 Reorder the terms: 0 = 14 + -11y + y2 Solving 0 = 14 + -11y + y2 Solving for variable 'y'. Combine like terms: 0 + -14 = -14 -14 + 11y + -1y2 = 14 + -11y + y2 + -14 + 11y + -1y2 Reorder the terms: -14 + 11y + -1y2 = 14 + -14 + -11y + 11y + y2 + -1y2 Combine like terms: 14 + -14 = 0 -14 + 11y + -1y2 = 0 + -11y + 11y + y2 + -1y2 -14 + 11y + -1y2 = -11y + 11y + y2 + -1y2 Combine like terms: -11y + 11y = 0 -14 + 11y + -1y2 = 0 + y2 + -1y2 -14 + 11y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 -14 + 11y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 14 + -11y + y2 = 0 Move the constant term to the right: Add '-14' to each side of the equation. 14 + -11y + -14 + y2 = 0 + -14 Reorder the terms: 14 + -14 + -11y + y2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -11y + y2 = 0 + -14 -11y + y2 = 0 + -14 Combine like terms: 0 + -14 = -14 -11y + y2 = -14 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 = -14 + 30.25 Reorder the terms: 30.25 + -11y + y2 = -14 + 30.25 Combine like terms: -14 + 30.25 = 16.25 30.25 + -11y + y2 = 16.25 Factor a perfect square on the left side: (y + -5.5)(y + -5.5) = 16.25 Calculate the square root of the right side: 4.031128874 Break this problem into two subproblems by setting (y + -5.5) equal to 4.031128874 and -4.031128874.Subproblem 1
y + -5.5 = 4.031128874 Simplifying y + -5.5 = 4.031128874 Reorder the terms: -5.5 + y = 4.031128874 Solving -5.5 + y = 4.031128874 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 = 4.031128874 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + y = 4.031128874 + 5.5 y = 4.031128874 + 5.5 Combine like terms: 4.031128874 + 5.5 = 9.531128874 y = 9.531128874 Simplifying y = 9.531128874Subproblem 2
y + -5.5 = -4.031128874 Simplifying y + -5.5 = -4.031128874 Reorder the terms: -5.5 + y = -4.031128874 Solving -5.5 + y = -4.031128874 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 = -4.031128874 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + y = -4.031128874 + 5.5 y = -4.031128874 + 5.5 Combine like terms: -4.031128874 + 5.5 = 1.468871126 y = 1.468871126 Simplifying y = 1.468871126Solution
The solution to the problem is based on the solutions from the subproblems. y = {9.531128874, 1.468871126}
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