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Simplifying 2w2 + -28w = 98 Reorder the terms: -28w + 2w2 = 98 Solving -28w + 2w2 = 98 Solving for variable 'w'. Reorder the terms: -98 + -28w + 2w2 = 98 + -98 Combine like terms: 98 + -98 = 0 -98 + -28w + 2w2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-49 + -14w + w2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-49 + -14w + w2)' equal to zero and attempt to solve: Simplifying -49 + -14w + w2 = 0 Solving -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 = 16.899494937 w = 16.899494937 Simplifying w = 16.899494937Subproblem 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 = -2.899494937 w = -2.899494937 Simplifying w = -2.899494937Solution
The solution to the problem is based on the solutions from the subproblems. w = {16.899494937, -2.899494937}Solution
w = {16.899494937, -2.899494937}
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