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Simplifying 0 = w2 + -14w + 38 Reorder the terms: 0 = 38 + -14w + w2 Solving 0 = 38 + -14w + w2 Solving for variable 'w'. Combine like terms: 0 + -38 = -38 -38 + 14w + -1w2 = 38 + -14w + w2 + -38 + 14w + -1w2 Reorder the terms: -38 + 14w + -1w2 = 38 + -38 + -14w + 14w + w2 + -1w2 Combine like terms: 38 + -38 = 0 -38 + 14w + -1w2 = 0 + -14w + 14w + w2 + -1w2 -38 + 14w + -1w2 = -14w + 14w + w2 + -1w2 Combine like terms: -14w + 14w = 0 -38 + 14w + -1w2 = 0 + w2 + -1w2 -38 + 14w + -1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 -38 + 14w + -1w2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 38 + -14w + w2 = 0 Move the constant term to the right: Add '-38' to each side of the equation. 38 + -14w + -38 + w2 = 0 + -38 Reorder the terms: 38 + -38 + -14w + w2 = 0 + -38 Combine like terms: 38 + -38 = 0 0 + -14w + w2 = 0 + -38 -14w + w2 = 0 + -38 Combine like terms: 0 + -38 = -38 -14w + w2 = -38 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 = -38 + 49 Reorder the terms: 49 + -14w + w2 = -38 + 49 Combine like terms: -38 + 49 = 11 49 + -14w + w2 = 11 Factor a perfect square on the left side: (w + -7)(w + -7) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (w + -7) equal to 3.31662479 and -3.31662479.Subproblem 1
w + -7 = 3.31662479 Simplifying w + -7 = 3.31662479 Reorder the terms: -7 + w = 3.31662479 Solving -7 + w = 3.31662479 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 = 3.31662479 + 7 Combine like terms: -7 + 7 = 0 0 + w = 3.31662479 + 7 w = 3.31662479 + 7 Combine like terms: 3.31662479 + 7 = 10.31662479 w = 10.31662479 Simplifying w = 10.31662479Subproblem 2
w + -7 = -3.31662479 Simplifying w + -7 = -3.31662479 Reorder the terms: -7 + w = -3.31662479 Solving -7 + w = -3.31662479 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 = -3.31662479 + 7 Combine like terms: -7 + 7 = 0 0 + w = -3.31662479 + 7 w = -3.31662479 + 7 Combine like terms: -3.31662479 + 7 = 3.68337521 w = 3.68337521 Simplifying w = 3.68337521Solution
The solution to the problem is based on the solutions from the subproblems. w = {10.31662479, 3.68337521}
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