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Simplifying w2 + 7w + -35 = 0 Reorder the terms: -35 + 7w + w2 = 0 Solving -35 + 7w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '35' to each side of the equation. -35 + 7w + 35 + w2 = 0 + 35 Reorder the terms: -35 + 35 + 7w + w2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + 7w + w2 = 0 + 35 7w + w2 = 0 + 35 Combine like terms: 0 + 35 = 35 7w + w2 = 35 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 = 35 + 12.25 Reorder the terms: 12.25 + 7w + w2 = 35 + 12.25 Combine like terms: 35 + 12.25 = 47.25 12.25 + 7w + w2 = 47.25 Factor a perfect square on the left side: (w + 3.5)(w + 3.5) = 47.25 Calculate the square root of the right side: 6.873863542 Break this problem into two subproblems by setting (w + 3.5) equal to 6.873863542 and -6.873863542.Subproblem 1
w + 3.5 = 6.873863542 Simplifying w + 3.5 = 6.873863542 Reorder the terms: 3.5 + w = 6.873863542 Solving 3.5 + w = 6.873863542 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 = 6.873863542 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + w = 6.873863542 + -3.5 w = 6.873863542 + -3.5 Combine like terms: 6.873863542 + -3.5 = 3.373863542 w = 3.373863542 Simplifying w = 3.373863542Subproblem 2
w + 3.5 = -6.873863542 Simplifying w + 3.5 = -6.873863542 Reorder the terms: 3.5 + w = -6.873863542 Solving 3.5 + w = -6.873863542 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 = -6.873863542 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + w = -6.873863542 + -3.5 w = -6.873863542 + -3.5 Combine like terms: -6.873863542 + -3.5 = -10.373863542 w = -10.373863542 Simplifying w = -10.373863542Solution
The solution to the problem is based on the solutions from the subproblems. w = {3.373863542, -10.373863542}
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