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Simplifying -1y2 + 11y = 8 Reorder the terms: 11y + -1y2 = 8 Solving 11y + -1y2 = 8 Solving for variable 'y'. Reorder the terms: -8 + 11y + -1y2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + 11y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 8 + -11y + y2 = 0 Move the constant term to the right: Add '-8' to each side of the equation. 8 + -11y + -8 + y2 = 0 + -8 Reorder the terms: 8 + -8 + -11y + y2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -11y + y2 = 0 + -8 -11y + y2 = 0 + -8 Combine like terms: 0 + -8 = -8 -11y + y2 = -8 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 = -8 + 30.25 Reorder the terms: 30.25 + -11y + y2 = -8 + 30.25 Combine like terms: -8 + 30.25 = 22.25 30.25 + -11y + y2 = 22.25 Factor a perfect square on the left side: (y + -5.5)(y + -5.5) = 22.25 Calculate the square root of the right side: 4.716990566 Break this problem into two subproblems by setting (y + -5.5) equal to 4.716990566 and -4.716990566.Subproblem 1
y + -5.5 = 4.716990566 Simplifying y + -5.5 = 4.716990566 Reorder the terms: -5.5 + y = 4.716990566 Solving -5.5 + y = 4.716990566 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 = 4.716990566 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + y = 4.716990566 + 5.5 y = 4.716990566 + 5.5 Combine like terms: 4.716990566 + 5.5 = 10.216990566 y = 10.216990566 Simplifying y = 10.216990566Subproblem 2
y + -5.5 = -4.716990566 Simplifying y + -5.5 = -4.716990566 Reorder the terms: -5.5 + y = -4.716990566 Solving -5.5 + y = -4.716990566 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 = -4.716990566 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + y = -4.716990566 + 5.5 y = -4.716990566 + 5.5 Combine like terms: -4.716990566 + 5.5 = 0.783009434 y = 0.783009434 Simplifying y = 0.783009434Solution
The solution to the problem is based on the solutions from the subproblems. y = {10.216990566, 0.783009434}
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