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Simplifying w2 + -14w = 47 Reorder the terms: -14w + w2 = 47 Solving -14w + w2 = 47 Solving for variable 'w'. Reorder the terms: -47 + -14w + w2 = 47 + -47 Combine like terms: 47 + -47 = 0 -47 + -14w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '47' to each side of the equation. -47 + -14w + 47 + w2 = 0 + 47 Reorder the terms: -47 + 47 + -14w + w2 = 0 + 47 Combine like terms: -47 + 47 = 0 0 + -14w + w2 = 0 + 47 -14w + w2 = 0 + 47 Combine like terms: 0 + 47 = 47 -14w + w2 = 47 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 = 47 + 49 Reorder the terms: 49 + -14w + w2 = 47 + 49 Combine like terms: 47 + 49 = 96 49 + -14w + w2 = 96 Factor a perfect square on the left side: (w + -7)(w + -7) = 96 Calculate the square root of the right side: 9.797958971 Break this problem into two subproblems by setting (w + -7) equal to 9.797958971 and -9.797958971.Subproblem 1
w + -7 = 9.797958971 Simplifying w + -7 = 9.797958971 Reorder the terms: -7 + w = 9.797958971 Solving -7 + w = 9.797958971 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 = 9.797958971 + 7 Combine like terms: -7 + 7 = 0 0 + w = 9.797958971 + 7 w = 9.797958971 + 7 Combine like terms: 9.797958971 + 7 = 16.797958971 w = 16.797958971 Simplifying w = 16.797958971Subproblem 2
w + -7 = -9.797958971 Simplifying w + -7 = -9.797958971 Reorder the terms: -7 + w = -9.797958971 Solving -7 + w = -9.797958971 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 = -9.797958971 + 7 Combine like terms: -7 + 7 = 0 0 + w = -9.797958971 + 7 w = -9.797958971 + 7 Combine like terms: -9.797958971 + 7 = -2.797958971 w = -2.797958971 Simplifying w = -2.797958971Solution
The solution to the problem is based on the solutions from the subproblems. w = {16.797958971, -2.797958971}
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