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Simplifying y(70 + -1y) + y = 11 (70 * y + -1y * y) + y = 11 (70y + -1y2) + y = 11 Reorder the terms: 70y + y + -1y2 = 11 Combine like terms: 70y + y = 71y 71y + -1y2 = 11 Solving 71y + -1y2 = 11 Solving for variable 'y'. Reorder the terms: -11 + 71y + -1y2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + 71y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 11 + -71y + y2 = 0 Move the constant term to the right: Add '-11' to each side of the equation. 11 + -71y + -11 + y2 = 0 + -11 Reorder the terms: 11 + -11 + -71y + y2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -71y + y2 = 0 + -11 -71y + y2 = 0 + -11 Combine like terms: 0 + -11 = -11 -71y + y2 = -11 The y term is -71y. Take half its coefficient (-35.5). Square it (1260.25) and add it to both sides. Add '1260.25' to each side of the equation. -71y + 1260.25 + y2 = -11 + 1260.25 Reorder the terms: 1260.25 + -71y + y2 = -11 + 1260.25 Combine like terms: -11 + 1260.25 = 1249.25 1260.25 + -71y + y2 = 1249.25 Factor a perfect square on the left side: (y + -35.5)(y + -35.5) = 1249.25 Calculate the square root of the right side: 35.344730866 Break this problem into two subproblems by setting (y + -35.5) equal to 35.344730866 and -35.344730866.Subproblem 1
y + -35.5 = 35.344730866 Simplifying y + -35.5 = 35.344730866 Reorder the terms: -35.5 + y = 35.344730866 Solving -35.5 + y = 35.344730866 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '35.5' to each side of the equation. -35.5 + 35.5 + y = 35.344730866 + 35.5 Combine like terms: -35.5 + 35.5 = 0.0 0.0 + y = 35.344730866 + 35.5 y = 35.344730866 + 35.5 Combine like terms: 35.344730866 + 35.5 = 70.844730866 y = 70.844730866 Simplifying y = 70.844730866Subproblem 2
y + -35.5 = -35.344730866 Simplifying y + -35.5 = -35.344730866 Reorder the terms: -35.5 + y = -35.344730866 Solving -35.5 + y = -35.344730866 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '35.5' to each side of the equation. -35.5 + 35.5 + y = -35.344730866 + 35.5 Combine like terms: -35.5 + 35.5 = 0.0 0.0 + y = -35.344730866 + 35.5 y = -35.344730866 + 35.5 Combine like terms: -35.344730866 + 35.5 = 0.155269134 y = 0.155269134 Simplifying y = 0.155269134Solution
The solution to the problem is based on the solutions from the subproblems. y = {70.844730866, 0.155269134}
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