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Simplifying ((-4w2) + 7w + -3) + ((5w2) + 2w + 1) = 0 Reorder the terms: (-3 + 7w + (-4w2)) + ((5w2) + 2w + 1) = 0 Remove parenthesis around (-3 + 7w + (-4w2)) -3 + 7w + (-4w2) + ((5w2) + 2w + 1) = 0 Reorder the terms: -3 + 7w + (-4w2) + (1 + 2w + (5w2)) = 0 Remove parenthesis around (1 + 2w + (5w2)) -3 + 7w + (-4w2) + 1 + 2w + (5w2) = 0 Reorder the terms: -3 + 1 + 7w + 2w + (-4w2) + (5w2) = 0 Combine like terms: -3 + 1 = -2 -2 + 7w + 2w + (-4w2) + (5w2) = 0 Combine like terms: 7w + 2w = 9w -2 + 9w + (-4w2) + (5w2) = 0 Combine like terms: (-4w2) + (5w2) = 1w2 -2 + 9w + 1w2 = 0 Solving -2 + 9w + 1w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + 9w + 2 + w2 = 0 + 2 Reorder the terms: -2 + 2 + 9w + w2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 9w + w2 = 0 + 2 9w + w2 = 0 + 2 Combine like terms: 0 + 2 = 2 9w + w2 = 2 The w term is 9w. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9w + 20.25 + w2 = 2 + 20.25 Reorder the terms: 20.25 + 9w + w2 = 2 + 20.25 Combine like terms: 2 + 20.25 = 22.25 20.25 + 9w + w2 = 22.25 Factor a perfect square on the left side: (w + 4.5)(w + 4.5) = 22.25 Calculate the square root of the right side: 4.716990566 Break this problem into two subproblems by setting (w + 4.5) equal to 4.716990566 and -4.716990566.Subproblem 1
w + 4.5 = 4.716990566 Simplifying w + 4.5 = 4.716990566 Reorder the terms: 4.5 + w = 4.716990566 Solving 4.5 + w = 4.716990566 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + w = 4.716990566 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + w = 4.716990566 + -4.5 w = 4.716990566 + -4.5 Combine like terms: 4.716990566 + -4.5 = 0.216990566 w = 0.216990566 Simplifying w = 0.216990566Subproblem 2
w + 4.5 = -4.716990566 Simplifying w + 4.5 = -4.716990566 Reorder the terms: 4.5 + w = -4.716990566 Solving 4.5 + w = -4.716990566 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + w = -4.716990566 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + w = -4.716990566 + -4.5 w = -4.716990566 + -4.5 Combine like terms: -4.716990566 + -4.5 = -9.216990566 w = -9.216990566 Simplifying w = -9.216990566Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.216990566, -9.216990566}
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