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Simplifying w + w2 + 6 = 24 Reorder the terms: 6 + w + w2 = 24 Solving 6 + w + w2 = 24 Solving for variable 'w'. Reorder the terms: 6 + -24 + w + w2 = 24 + -24 Combine like terms: 6 + -24 = -18 -18 + w + w2 = 24 + -24 Combine like terms: 24 + -24 = 0 -18 + w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + w + 18 + w2 = 0 + 18 Reorder the terms: -18 + 18 + w + w2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + w + w2 = 0 + 18 w + w2 = 0 + 18 Combine like terms: 0 + 18 = 18 w + w2 = 18 The w term is w. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. w + 0.25 + w2 = 18 + 0.25 Reorder the terms: 0.25 + w + w2 = 18 + 0.25 Combine like terms: 18 + 0.25 = 18.25 0.25 + w + w2 = 18.25 Factor a perfect square on the left side: (w + 0.5)(w + 0.5) = 18.25 Calculate the square root of the right side: 4.272001873 Break this problem into two subproblems by setting (w + 0.5) equal to 4.272001873 and -4.272001873.Subproblem 1
w + 0.5 = 4.272001873 Simplifying w + 0.5 = 4.272001873 Reorder the terms: 0.5 + w = 4.272001873 Solving 0.5 + w = 4.272001873 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + w = 4.272001873 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w = 4.272001873 + -0.5 w = 4.272001873 + -0.5 Combine like terms: 4.272001873 + -0.5 = 3.772001873 w = 3.772001873 Simplifying w = 3.772001873Subproblem 2
w + 0.5 = -4.272001873 Simplifying w + 0.5 = -4.272001873 Reorder the terms: 0.5 + w = -4.272001873 Solving 0.5 + w = -4.272001873 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + w = -4.272001873 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w = -4.272001873 + -0.5 w = -4.272001873 + -0.5 Combine like terms: -4.272001873 + -0.5 = -4.772001873 w = -4.772001873 Simplifying w = -4.772001873Solution
The solution to the problem is based on the solutions from the subproblems. w = {3.772001873, -4.772001873}
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