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Simplifying 0 = w2 + -2w + -54 Reorder the terms: 0 = -54 + -2w + w2 Solving 0 = -54 + -2w + w2 Solving for variable 'w'. Combine like terms: 0 + 54 = 54 54 + 2w + -1w2 = -54 + -2w + w2 + 54 + 2w + -1w2 Reorder the terms: 54 + 2w + -1w2 = -54 + 54 + -2w + 2w + w2 + -1w2 Combine like terms: -54 + 54 = 0 54 + 2w + -1w2 = 0 + -2w + 2w + w2 + -1w2 54 + 2w + -1w2 = -2w + 2w + w2 + -1w2 Combine like terms: -2w + 2w = 0 54 + 2w + -1w2 = 0 + w2 + -1w2 54 + 2w + -1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 54 + 2w + -1w2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -54 + -2w + w2 = 0 Move the constant term to the right: Add '54' to each side of the equation. -54 + -2w + 54 + w2 = 0 + 54 Reorder the terms: -54 + 54 + -2w + w2 = 0 + 54 Combine like terms: -54 + 54 = 0 0 + -2w + w2 = 0 + 54 -2w + w2 = 0 + 54 Combine like terms: 0 + 54 = 54 -2w + w2 = 54 The w term is -2w. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2w + 1 + w2 = 54 + 1 Reorder the terms: 1 + -2w + w2 = 54 + 1 Combine like terms: 54 + 1 = 55 1 + -2w + w2 = 55 Factor a perfect square on the left side: (w + -1)(w + -1) = 55 Calculate the square root of the right side: 7.416198487 Break this problem into two subproblems by setting (w + -1) equal to 7.416198487 and -7.416198487.Subproblem 1
w + -1 = 7.416198487 Simplifying w + -1 = 7.416198487 Reorder the terms: -1 + w = 7.416198487 Solving -1 + w = 7.416198487 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + w = 7.416198487 + 1 Combine like terms: -1 + 1 = 0 0 + w = 7.416198487 + 1 w = 7.416198487 + 1 Combine like terms: 7.416198487 + 1 = 8.416198487 w = 8.416198487 Simplifying w = 8.416198487Subproblem 2
w + -1 = -7.416198487 Simplifying w + -1 = -7.416198487 Reorder the terms: -1 + w = -7.416198487 Solving -1 + w = -7.416198487 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + w = -7.416198487 + 1 Combine like terms: -1 + 1 = 0 0 + w = -7.416198487 + 1 w = -7.416198487 + 1 Combine like terms: -7.416198487 + 1 = -6.416198487 w = -6.416198487 Simplifying w = -6.416198487Solution
The solution to the problem is based on the solutions from the subproblems. w = {8.416198487, -6.416198487}
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