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Simplifying w2 + -7w + 8 = 0 Reorder the terms: 8 + -7w + w2 = 0 Solving 8 + -7w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + -7w + -8 + w2 = 0 + -8 Reorder the terms: 8 + -8 + -7w + w2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -7w + w2 = 0 + -8 -7w + w2 = 0 + -8 Combine like terms: 0 + -8 = -8 -7w + w2 = -8 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 = -8 + 12.25 Reorder the terms: 12.25 + -7w + w2 = -8 + 12.25 Combine like terms: -8 + 12.25 = 4.25 12.25 + -7w + w2 = 4.25 Factor a perfect square on the left side: (w + -3.5)(w + -3.5) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (w + -3.5) equal to 2.061552813 and -2.061552813.Subproblem 1
w + -3.5 = 2.061552813 Simplifying w + -3.5 = 2.061552813 Reorder the terms: -3.5 + w = 2.061552813 Solving -3.5 + w = 2.061552813 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 = 2.061552813 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + w = 2.061552813 + 3.5 w = 2.061552813 + 3.5 Combine like terms: 2.061552813 + 3.5 = 5.561552813 w = 5.561552813 Simplifying w = 5.561552813Subproblem 2
w + -3.5 = -2.061552813 Simplifying w + -3.5 = -2.061552813 Reorder the terms: -3.5 + w = -2.061552813 Solving -3.5 + w = -2.061552813 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 = -2.061552813 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + w = -2.061552813 + 3.5 w = -2.061552813 + 3.5 Combine like terms: -2.061552813 + 3.5 = 1.438447187 w = 1.438447187 Simplifying w = 1.438447187Solution
The solution to the problem is based on the solutions from the subproblems. w = {5.561552813, 1.438447187}
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