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Simplifying w2 + 14w = 49 Reorder the terms: 14w + w2 = 49 Solving 14w + w2 = 49 Solving for variable 'w'. Reorder the terms: -49 + 14w + w2 = 49 + -49 Combine like terms: 49 + -49 = 0 -49 + 14w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '49' to each side of the equation. -49 + 14w + 49 + w2 = 0 + 49 Reorder the terms: -49 + 49 + 14w + w2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + 14w + w2 = 0 + 49 14w + w2 = 0 + 49 Combine like terms: 0 + 49 = 49 14w + w2 = 49 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 = 49 + 49 Reorder the terms: 49 + 14w + w2 = 49 + 49 Combine like terms: 49 + 49 = 98 49 + 14w + w2 = 98 Factor a perfect square on the left side: (w + 7)(w + 7) = 98 Calculate the square root of the right side: 9.899494937 Break this problem into two subproblems by setting (w + 7) equal to 9.899494937 and -9.899494937.Subproblem 1
w + 7 = 9.899494937 Simplifying w + 7 = 9.899494937 Reorder the terms: 7 + w = 9.899494937 Solving 7 + w = 9.899494937 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 = 9.899494937 + -7 Combine like terms: 7 + -7 = 0 0 + w = 9.899494937 + -7 w = 9.899494937 + -7 Combine like terms: 9.899494937 + -7 = 2.899494937 w = 2.899494937 Simplifying w = 2.899494937Subproblem 2
w + 7 = -9.899494937 Simplifying w + 7 = -9.899494937 Reorder the terms: 7 + w = -9.899494937 Solving 7 + w = -9.899494937 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 = -9.899494937 + -7 Combine like terms: 7 + -7 = 0 0 + w = -9.899494937 + -7 w = -9.899494937 + -7 Combine like terms: -9.899494937 + -7 = -16.899494937 w = -16.899494937 Simplifying w = -16.899494937Solution
The solution to the problem is based on the solutions from the subproblems. w = {2.899494937, -16.899494937}
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