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Simplifying w2 + 14w + 49 = 8 Reorder the terms: 49 + 14w + w2 = 8 Solving 49 + 14w + w2 = 8 Solving for variable 'w'. Reorder the terms: 49 + -8 + 14w + w2 = 8 + -8 Combine like terms: 49 + -8 = 41 41 + 14w + w2 = 8 + -8 Combine like terms: 8 + -8 = 0 41 + 14w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '-41' to each side of the equation. 41 + 14w + -41 + w2 = 0 + -41 Reorder the terms: 41 + -41 + 14w + w2 = 0 + -41 Combine like terms: 41 + -41 = 0 0 + 14w + w2 = 0 + -41 14w + w2 = 0 + -41 Combine like terms: 0 + -41 = -41 14w + w2 = -41 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 = -41 + 49 Reorder the terms: 49 + 14w + w2 = -41 + 49 Combine like terms: -41 + 49 = 8 49 + 14w + w2 = 8 Factor a perfect square on the left side: (w + 7)(w + 7) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (w + 7) equal to 2.828427125 and -2.828427125.Subproblem 1
w + 7 = 2.828427125 Simplifying w + 7 = 2.828427125 Reorder the terms: 7 + w = 2.828427125 Solving 7 + w = 2.828427125 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 = 2.828427125 + -7 Combine like terms: 7 + -7 = 0 0 + w = 2.828427125 + -7 w = 2.828427125 + -7 Combine like terms: 2.828427125 + -7 = -4.171572875 w = -4.171572875 Simplifying w = -4.171572875Subproblem 2
w + 7 = -2.828427125 Simplifying w + 7 = -2.828427125 Reorder the terms: 7 + w = -2.828427125 Solving 7 + w = -2.828427125 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 = -2.828427125 + -7 Combine like terms: 7 + -7 = 0 0 + w = -2.828427125 + -7 w = -2.828427125 + -7 Combine like terms: -2.828427125 + -7 = -9.828427125 w = -9.828427125 Simplifying w = -9.828427125Solution
The solution to the problem is based on the solutions from the subproblems. w = {-4.171572875, -9.828427125}
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