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Simplifying w2 + 14w = 11 Reorder the terms: 14w + w2 = 11 Solving 14w + w2 = 11 Solving for variable 'w'. Reorder the terms: -11 + 14w + w2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + 14w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + 14w + 11 + w2 = 0 + 11 Reorder the terms: -11 + 11 + 14w + w2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 14w + w2 = 0 + 11 14w + w2 = 0 + 11 Combine like terms: 0 + 11 = 11 14w + w2 = 11 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 = 11 + 49 Reorder the terms: 49 + 14w + w2 = 11 + 49 Combine like terms: 11 + 49 = 60 49 + 14w + w2 = 60 Factor a perfect square on the left side: (w + 7)(w + 7) = 60 Calculate the square root of the right side: 7.745966692 Break this problem into two subproblems by setting (w + 7) equal to 7.745966692 and -7.745966692.Subproblem 1
w + 7 = 7.745966692 Simplifying w + 7 = 7.745966692 Reorder the terms: 7 + w = 7.745966692 Solving 7 + w = 7.745966692 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 = 7.745966692 + -7 Combine like terms: 7 + -7 = 0 0 + w = 7.745966692 + -7 w = 7.745966692 + -7 Combine like terms: 7.745966692 + -7 = 0.745966692 w = 0.745966692 Simplifying w = 0.745966692Subproblem 2
w + 7 = -7.745966692 Simplifying w + 7 = -7.745966692 Reorder the terms: 7 + w = -7.745966692 Solving 7 + w = -7.745966692 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 = -7.745966692 + -7 Combine like terms: 7 + -7 = 0 0 + w = -7.745966692 + -7 w = -7.745966692 + -7 Combine like terms: -7.745966692 + -7 = -14.745966692 w = -14.745966692 Simplifying w = -14.745966692Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.745966692, -14.745966692}
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