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Simplifying 368 = w2 + 24w Reorder the terms: 368 = 24w + w2 Solving 368 = 24w + w2 Solving for variable 'w'. Reorder the terms: 368 + -24w + -1w2 = 24w + -24w + w2 + -1w2 Combine like terms: 24w + -24w = 0 368 + -24w + -1w2 = 0 + w2 + -1w2 368 + -24w + -1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 368 + -24w + -1w2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -368 + 24w + w2 = 0 Move the constant term to the right: Add '368' to each side of the equation. -368 + 24w + 368 + w2 = 0 + 368 Reorder the terms: -368 + 368 + 24w + w2 = 0 + 368 Combine like terms: -368 + 368 = 0 0 + 24w + w2 = 0 + 368 24w + w2 = 0 + 368 Combine like terms: 0 + 368 = 368 24w + w2 = 368 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 = 368 + 144 Reorder the terms: 144 + 24w + w2 = 368 + 144 Combine like terms: 368 + 144 = 512 144 + 24w + w2 = 512 Factor a perfect square on the left side: (w + 12)(w + 12) = 512 Calculate the square root of the right side: 22.627416998 Break this problem into two subproblems by setting (w + 12) equal to 22.627416998 and -22.627416998.Subproblem 1
w + 12 = 22.627416998 Simplifying w + 12 = 22.627416998 Reorder the terms: 12 + w = 22.627416998 Solving 12 + w = 22.627416998 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 = 22.627416998 + -12 Combine like terms: 12 + -12 = 0 0 + w = 22.627416998 + -12 w = 22.627416998 + -12 Combine like terms: 22.627416998 + -12 = 10.627416998 w = 10.627416998 Simplifying w = 10.627416998Subproblem 2
w + 12 = -22.627416998 Simplifying w + 12 = -22.627416998 Reorder the terms: 12 + w = -22.627416998 Solving 12 + w = -22.627416998 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 = -22.627416998 + -12 Combine like terms: 12 + -12 = 0 0 + w = -22.627416998 + -12 w = -22.627416998 + -12 Combine like terms: -22.627416998 + -12 = -34.627416998 w = -34.627416998 Simplifying w = -34.627416998Solution
The solution to the problem is based on the solutions from the subproblems. w = {10.627416998, -34.627416998}
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