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Simplifying (w + 7)(w + 7) + -54 = 0 Reorder the terms: (7 + w)(w + 7) + -54 = 0 Reorder the terms: (7 + w)(7 + w) + -54 = 0 Multiply (7 + w) * (7 + w) (7(7 + w) + w(7 + w)) + -54 = 0 ((7 * 7 + w * 7) + w(7 + w)) + -54 = 0 ((49 + 7w) + w(7 + w)) + -54 = 0 (49 + 7w + (7 * w + w * w)) + -54 = 0 (49 + 7w + (7w + w2)) + -54 = 0 Combine like terms: 7w + 7w = 14w (49 + 14w + w2) + -54 = 0 Reorder the terms: 49 + -54 + 14w + w2 = 0 Combine like terms: 49 + -54 = -5 -5 + 14w + w2 = 0 Solving -5 + 14w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + 14w + 5 + w2 = 0 + 5 Reorder the terms: -5 + 5 + 14w + w2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 14w + w2 = 0 + 5 14w + w2 = 0 + 5 Combine like terms: 0 + 5 = 5 14w + w2 = 5 The w term is 14w. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14w + 49 + w2 = 5 + 49 Reorder the terms: 49 + 14w + w2 = 5 + 49 Combine like terms: 5 + 49 = 54 49 + 14w + w2 = 54 Factor a perfect square on the left side: (w + 7)(w + 7) = 54 Calculate the square root of the right side: 7.348469228 Break this problem into two subproblems by setting (w + 7) equal to 7.348469228 and -7.348469228.Subproblem 1
w + 7 = 7.348469228 Simplifying w + 7 = 7.348469228 Reorder the terms: 7 + w = 7.348469228 Solving 7 + w = 7.348469228 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + w = 7.348469228 + -7 Combine like terms: 7 + -7 = 0 0 + w = 7.348469228 + -7 w = 7.348469228 + -7 Combine like terms: 7.348469228 + -7 = 0.348469228 w = 0.348469228 Simplifying w = 0.348469228Subproblem 2
w + 7 = -7.348469228 Simplifying w + 7 = -7.348469228 Reorder the terms: 7 + w = -7.348469228 Solving 7 + w = -7.348469228 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + w = -7.348469228 + -7 Combine like terms: 7 + -7 = 0 0 + w = -7.348469228 + -7 w = -7.348469228 + -7 Combine like terms: -7.348469228 + -7 = -14.348469228 w = -14.348469228 Simplifying w = -14.348469228Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.348469228, -14.348469228}
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