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Simplifying 48 = w2 + 6w + 4 Reorder the terms: 48 = 4 + 6w + w2 Solving 48 = 4 + 6w + w2 Solving for variable 'w'. Combine like terms: 48 + -4 = 44 44 + -6w + -1w2 = 4 + 6w + w2 + -4 + -6w + -1w2 Reorder the terms: 44 + -6w + -1w2 = 4 + -4 + 6w + -6w + w2 + -1w2 Combine like terms: 4 + -4 = 0 44 + -6w + -1w2 = 0 + 6w + -6w + w2 + -1w2 44 + -6w + -1w2 = 6w + -6w + w2 + -1w2 Combine like terms: 6w + -6w = 0 44 + -6w + -1w2 = 0 + w2 + -1w2 44 + -6w + -1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 44 + -6w + -1w2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -44 + 6w + w2 = 0 Move the constant term to the right: Add '44' to each side of the equation. -44 + 6w + 44 + w2 = 0 + 44 Reorder the terms: -44 + 44 + 6w + w2 = 0 + 44 Combine like terms: -44 + 44 = 0 0 + 6w + w2 = 0 + 44 6w + w2 = 0 + 44 Combine like terms: 0 + 44 = 44 6w + w2 = 44 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 = 44 + 9 Reorder the terms: 9 + 6w + w2 = 44 + 9 Combine like terms: 44 + 9 = 53 9 + 6w + w2 = 53 Factor a perfect square on the left side: (w + 3)(w + 3) = 53 Calculate the square root of the right side: 7.280109889 Break this problem into two subproblems by setting (w + 3) equal to 7.280109889 and -7.280109889.Subproblem 1
w + 3 = 7.280109889 Simplifying w + 3 = 7.280109889 Reorder the terms: 3 + w = 7.280109889 Solving 3 + w = 7.280109889 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 = 7.280109889 + -3 Combine like terms: 3 + -3 = 0 0 + w = 7.280109889 + -3 w = 7.280109889 + -3 Combine like terms: 7.280109889 + -3 = 4.280109889 w = 4.280109889 Simplifying w = 4.280109889Subproblem 2
w + 3 = -7.280109889 Simplifying w + 3 = -7.280109889 Reorder the terms: 3 + w = -7.280109889 Solving 3 + w = -7.280109889 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 = -7.280109889 + -3 Combine like terms: 3 + -3 = 0 0 + w = -7.280109889 + -3 w = -7.280109889 + -3 Combine like terms: -7.280109889 + -3 = -10.280109889 w = -10.280109889 Simplifying w = -10.280109889Solution
The solution to the problem is based on the solutions from the subproblems. w = {4.280109889, -10.280109889}
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