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Simplifying 2w2 + -11w + -42 = 0 Reorder the terms: -42 + -11w + 2w2 = 0 Solving -42 + -11w + 2w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -21 + -5.5w + w2 = 0 Move the constant term to the right: Add '21' to each side of the equation. -21 + -5.5w + 21 + w2 = 0 + 21 Reorder the terms: -21 + 21 + -5.5w + w2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + -5.5w + w2 = 0 + 21 -5.5w + w2 = 0 + 21 Combine like terms: 0 + 21 = 21 -5.5w + w2 = 21 The w term is -5.5w. Take half its coefficient (-2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. -5.5w + 7.5625 + w2 = 21 + 7.5625 Reorder the terms: 7.5625 + -5.5w + w2 = 21 + 7.5625 Combine like terms: 21 + 7.5625 = 28.5625 7.5625 + -5.5w + w2 = 28.5625 Factor a perfect square on the left side: (w + -2.75)(w + -2.75) = 28.5625 Calculate the square root of the right side: 5.344389582 Break this problem into two subproblems by setting (w + -2.75) equal to 5.344389582 and -5.344389582.Subproblem 1
w + -2.75 = 5.344389582 Simplifying w + -2.75 = 5.344389582 Reorder the terms: -2.75 + w = 5.344389582 Solving -2.75 + w = 5.344389582 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + w = 5.344389582 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + w = 5.344389582 + 2.75 w = 5.344389582 + 2.75 Combine like terms: 5.344389582 + 2.75 = 8.094389582 w = 8.094389582 Simplifying w = 8.094389582Subproblem 2
w + -2.75 = -5.344389582 Simplifying w + -2.75 = -5.344389582 Reorder the terms: -2.75 + w = -5.344389582 Solving -2.75 + w = -5.344389582 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + w = -5.344389582 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + w = -5.344389582 + 2.75 w = -5.344389582 + 2.75 Combine like terms: -5.344389582 + 2.75 = -2.594389582 w = -2.594389582 Simplifying w = -2.594389582Solution
The solution to the problem is based on the solutions from the subproblems. w = {8.094389582, -2.594389582}
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