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Simplifying 48 = (w)(w + 6) Reorder the terms: 48 = w(6 + w) 48 = (6 * w + w * w) 48 = (6w + w2) Solving 48 = 6w + w2 Solving for variable 'w'. Reorder the terms: 48 + -6w + -1w2 = 6w + -6w + w2 + -1w2 Combine like terms: 6w + -6w = 0 48 + -6w + -1w2 = 0 + w2 + -1w2 48 + -6w + -1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 48 + -6w + -1w2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -48 + 6w + w2 = 0 Move the constant term to the right: Add '48' to each side of the equation. -48 + 6w + 48 + w2 = 0 + 48 Reorder the terms: -48 + 48 + 6w + w2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + 6w + w2 = 0 + 48 6w + w2 = 0 + 48 Combine like terms: 0 + 48 = 48 6w + w2 = 48 The w term is 6w. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6w + 9 + w2 = 48 + 9 Reorder the terms: 9 + 6w + w2 = 48 + 9 Combine like terms: 48 + 9 = 57 9 + 6w + w2 = 57 Factor a perfect square on the left side: (w + 3)(w + 3) = 57 Calculate the square root of the right side: 7.549834435 Break this problem into two subproblems by setting (w + 3) equal to 7.549834435 and -7.549834435.Subproblem 1
w + 3 = 7.549834435 Simplifying w + 3 = 7.549834435 Reorder the terms: 3 + w = 7.549834435 Solving 3 + w = 7.549834435 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + w = 7.549834435 + -3 Combine like terms: 3 + -3 = 0 0 + w = 7.549834435 + -3 w = 7.549834435 + -3 Combine like terms: 7.549834435 + -3 = 4.549834435 w = 4.549834435 Simplifying w = 4.549834435Subproblem 2
w + 3 = -7.549834435 Simplifying w + 3 = -7.549834435 Reorder the terms: 3 + w = -7.549834435 Solving 3 + w = -7.549834435 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + w = -7.549834435 + -3 Combine like terms: 3 + -3 = 0 0 + w = -7.549834435 + -3 w = -7.549834435 + -3 Combine like terms: -7.549834435 + -3 = -10.549834435 w = -10.549834435 Simplifying w = -10.549834435Solution
The solution to the problem is based on the solutions from the subproblems. w = {4.549834435, -10.549834435}
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