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Simplifying (-3w2 + 7w + -1) + (5w2 + 6w + 2) = 0 Reorder the terms: (-1 + 7w + -3w2) + (5w2 + 6w + 2) = 0 Remove parenthesis around (-1 + 7w + -3w2) -1 + 7w + -3w2 + (5w2 + 6w + 2) = 0 Reorder the terms: -1 + 7w + -3w2 + (2 + 6w + 5w2) = 0 Remove parenthesis around (2 + 6w + 5w2) -1 + 7w + -3w2 + 2 + 6w + 5w2 = 0 Reorder the terms: -1 + 2 + 7w + 6w + -3w2 + 5w2 = 0 Combine like terms: -1 + 2 = 1 1 + 7w + 6w + -3w2 + 5w2 = 0 Combine like terms: 7w + 6w = 13w 1 + 13w + -3w2 + 5w2 = 0 Combine like terms: -3w2 + 5w2 = 2w2 1 + 13w + 2w2 = 0 Solving 1 + 13w + 2w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 0.5 + 6.5w + w2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + 6.5w + -0.5 + w2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + 6.5w + w2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + 6.5w + w2 = 0 + -0.5 6.5w + w2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 6.5w + w2 = -0.5 The w term is 6.5w. Take half its coefficient (3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. 6.5w + 10.5625 + w2 = -0.5 + 10.5625 Reorder the terms: 10.5625 + 6.5w + w2 = -0.5 + 10.5625 Combine like terms: -0.5 + 10.5625 = 10.0625 10.5625 + 6.5w + w2 = 10.0625 Factor a perfect square on the left side: (w + 3.25)(w + 3.25) = 10.0625 Calculate the square root of the right side: 3.172144385 Break this problem into two subproblems by setting (w + 3.25) equal to 3.172144385 and -3.172144385.Subproblem 1
w + 3.25 = 3.172144385 Simplifying w + 3.25 = 3.172144385 Reorder the terms: 3.25 + w = 3.172144385 Solving 3.25 + w = 3.172144385 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + w = 3.172144385 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + w = 3.172144385 + -3.25 w = 3.172144385 + -3.25 Combine like terms: 3.172144385 + -3.25 = -0.077855615 w = -0.077855615 Simplifying w = -0.077855615Subproblem 2
w + 3.25 = -3.172144385 Simplifying w + 3.25 = -3.172144385 Reorder the terms: 3.25 + w = -3.172144385 Solving 3.25 + w = -3.172144385 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + w = -3.172144385 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + w = -3.172144385 + -3.25 w = -3.172144385 + -3.25 Combine like terms: -3.172144385 + -3.25 = -6.422144385 w = -6.422144385 Simplifying w = -6.422144385Solution
The solution to the problem is based on the solutions from the subproblems. w = {-0.077855615, -6.422144385}
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