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Simplifying w2 + 7w = 4 Reorder the terms: 7w + w2 = 4 Solving 7w + w2 = 4 Solving for variable 'w'. Reorder the terms: -4 + 7w + w2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + 7w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + 7w + 4 + w2 = 0 + 4 Reorder the terms: -4 + 4 + 7w + w2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 7w + w2 = 0 + 4 7w + w2 = 0 + 4 Combine like terms: 0 + 4 = 4 7w + w2 = 4 The w term is 7w. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7w + 12.25 + w2 = 4 + 12.25 Reorder the terms: 12.25 + 7w + w2 = 4 + 12.25 Combine like terms: 4 + 12.25 = 16.25 12.25 + 7w + w2 = 16.25 Factor a perfect square on the left side: (w + 3.5)(w + 3.5) = 16.25 Calculate the square root of the right side: 4.031128874 Break this problem into two subproblems by setting (w + 3.5) equal to 4.031128874 and -4.031128874.Subproblem 1
w + 3.5 = 4.031128874 Simplifying w + 3.5 = 4.031128874 Reorder the terms: 3.5 + w = 4.031128874 Solving 3.5 + w = 4.031128874 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + w = 4.031128874 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + w = 4.031128874 + -3.5 w = 4.031128874 + -3.5 Combine like terms: 4.031128874 + -3.5 = 0.531128874 w = 0.531128874 Simplifying w = 0.531128874Subproblem 2
w + 3.5 = -4.031128874 Simplifying w + 3.5 = -4.031128874 Reorder the terms: 3.5 + w = -4.031128874 Solving 3.5 + w = -4.031128874 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + w = -4.031128874 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + w = -4.031128874 + -3.5 w = -4.031128874 + -3.5 Combine like terms: -4.031128874 + -3.5 = -7.531128874 w = -7.531128874 Simplifying w = -7.531128874Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.531128874, -7.531128874}
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