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Simplifying w2 + -24w + 24 = 0 Reorder the terms: 24 + -24w + w2 = 0 Solving 24 + -24w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '-24' to each side of the equation. 24 + -24w + -24 + w2 = 0 + -24 Reorder the terms: 24 + -24 + -24w + w2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + -24w + w2 = 0 + -24 -24w + w2 = 0 + -24 Combine like terms: 0 + -24 = -24 -24w + w2 = -24 The w term is -24w. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24w + 144 + w2 = -24 + 144 Reorder the terms: 144 + -24w + w2 = -24 + 144 Combine like terms: -24 + 144 = 120 144 + -24w + w2 = 120 Factor a perfect square on the left side: (w + -12)(w + -12) = 120 Calculate the square root of the right side: 10.95445115 Break this problem into two subproblems by setting (w + -12) equal to 10.95445115 and -10.95445115.Subproblem 1
w + -12 = 10.95445115 Simplifying w + -12 = 10.95445115 Reorder the terms: -12 + w = 10.95445115 Solving -12 + w = 10.95445115 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + w = 10.95445115 + 12 Combine like terms: -12 + 12 = 0 0 + w = 10.95445115 + 12 w = 10.95445115 + 12 Combine like terms: 10.95445115 + 12 = 22.95445115 w = 22.95445115 Simplifying w = 22.95445115Subproblem 2
w + -12 = -10.95445115 Simplifying w + -12 = -10.95445115 Reorder the terms: -12 + w = -10.95445115 Solving -12 + w = -10.95445115 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + w = -10.95445115 + 12 Combine like terms: -12 + 12 = 0 0 + w = -10.95445115 + 12 w = -10.95445115 + 12 Combine like terms: -10.95445115 + 12 = 1.04554885 w = 1.04554885 Simplifying w = 1.04554885Solution
The solution to the problem is based on the solutions from the subproblems. w = {22.95445115, 1.04554885}
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