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Simplifying w2 + 4w + -48 = 0 Reorder the terms: -48 + 4w + w2 = 0 Solving -48 + 4w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '48' to each side of the equation. -48 + 4w + 48 + w2 = 0 + 48 Reorder the terms: -48 + 48 + 4w + w2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + 4w + w2 = 0 + 48 4w + w2 = 0 + 48 Combine like terms: 0 + 48 = 48 4w + w2 = 48 The w term is 4w. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4w + 4 + w2 = 48 + 4 Reorder the terms: 4 + 4w + w2 = 48 + 4 Combine like terms: 48 + 4 = 52 4 + 4w + w2 = 52 Factor a perfect square on the left side: (w + 2)(w + 2) = 52 Calculate the square root of the right side: 7.211102551 Break this problem into two subproblems by setting (w + 2) equal to 7.211102551 and -7.211102551.Subproblem 1
w + 2 = 7.211102551 Simplifying w + 2 = 7.211102551 Reorder the terms: 2 + w = 7.211102551 Solving 2 + w = 7.211102551 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + w = 7.211102551 + -2 Combine like terms: 2 + -2 = 0 0 + w = 7.211102551 + -2 w = 7.211102551 + -2 Combine like terms: 7.211102551 + -2 = 5.211102551 w = 5.211102551 Simplifying w = 5.211102551Subproblem 2
w + 2 = -7.211102551 Simplifying w + 2 = -7.211102551 Reorder the terms: 2 + w = -7.211102551 Solving 2 + w = -7.211102551 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + w = -7.211102551 + -2 Combine like terms: 2 + -2 = 0 0 + w = -7.211102551 + -2 w = -7.211102551 + -2 Combine like terms: -7.211102551 + -2 = -9.211102551 w = -9.211102551 Simplifying w = -9.211102551Solution
The solution to the problem is based on the solutions from the subproblems. w = {5.211102551, -9.211102551}
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