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Simplifying 5w2 + -24w = -5 Reorder the terms: -24w + 5w2 = -5 Solving -24w + 5w2 = -5 Solving for variable 'w'. Reorder the terms: 5 + -24w + 5w2 = -5 + 5 Combine like terms: -5 + 5 = 0 5 + -24w + 5w2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1 + -4.8w + w2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -4.8w + -1 + w2 = 0 + -1 Reorder the terms: 1 + -1 + -4.8w + w2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4.8w + w2 = 0 + -1 -4.8w + w2 = 0 + -1 Combine like terms: 0 + -1 = -1 -4.8w + w2 = -1 The w term is -4.8w. Take half its coefficient (-2.4). Square it (5.76) and add it to both sides. Add '5.76' to each side of the equation. -4.8w + 5.76 + w2 = -1 + 5.76 Reorder the terms: 5.76 + -4.8w + w2 = -1 + 5.76 Combine like terms: -1 + 5.76 = 4.76 5.76 + -4.8w + w2 = 4.76 Factor a perfect square on the left side: (w + -2.4)(w + -2.4) = 4.76 Calculate the square root of the right side: 2.181742423 Break this problem into two subproblems by setting (w + -2.4) equal to 2.181742423 and -2.181742423.Subproblem 1
w + -2.4 = 2.181742423 Simplifying w + -2.4 = 2.181742423 Reorder the terms: -2.4 + w = 2.181742423 Solving -2.4 + w = 2.181742423 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2.4' to each side of the equation. -2.4 + 2.4 + w = 2.181742423 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + w = 2.181742423 + 2.4 w = 2.181742423 + 2.4 Combine like terms: 2.181742423 + 2.4 = 4.581742423 w = 4.581742423 Simplifying w = 4.581742423Subproblem 2
w + -2.4 = -2.181742423 Simplifying w + -2.4 = -2.181742423 Reorder the terms: -2.4 + w = -2.181742423 Solving -2.4 + w = -2.181742423 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2.4' to each side of the equation. -2.4 + 2.4 + w = -2.181742423 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + w = -2.181742423 + 2.4 w = -2.181742423 + 2.4 Combine like terms: -2.181742423 + 2.4 = 0.218257577 w = 0.218257577 Simplifying w = 0.218257577Solution
The solution to the problem is based on the solutions from the subproblems. w = {4.581742423, 0.218257577}
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