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Simplifying 3 = w(w + -6) + -7w Reorder the terms: 3 = w(-6 + w) + -7w 3 = (-6 * w + w * w) + -7w 3 = (-6w + w2) + -7w Reorder the terms: 3 = -6w + -7w + w2 Combine like terms: -6w + -7w = -13w 3 = -13w + w2 Solving 3 = -13w + w2 Solving for variable 'w'. Reorder the terms: 3 + 13w + -1w2 = -13w + 13w + w2 + -1w2 Combine like terms: -13w + 13w = 0 3 + 13w + -1w2 = 0 + w2 + -1w2 3 + 13w + -1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 3 + 13w + -1w2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -3 + -13w + w2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -13w + 3 + w2 = 0 + 3 Reorder the terms: -3 + 3 + -13w + w2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -13w + w2 = 0 + 3 -13w + w2 = 0 + 3 Combine like terms: 0 + 3 = 3 -13w + w2 = 3 The w term is -13w. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13w + 42.25 + w2 = 3 + 42.25 Reorder the terms: 42.25 + -13w + w2 = 3 + 42.25 Combine like terms: 3 + 42.25 = 45.25 42.25 + -13w + w2 = 45.25 Factor a perfect square on the left side: (w + -6.5)(w + -6.5) = 45.25 Calculate the square root of the right side: 6.726812024 Break this problem into two subproblems by setting (w + -6.5) equal to 6.726812024 and -6.726812024.Subproblem 1
w + -6.5 = 6.726812024 Simplifying w + -6.5 = 6.726812024 Reorder the terms: -6.5 + w = 6.726812024 Solving -6.5 + w = 6.726812024 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + w = 6.726812024 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + w = 6.726812024 + 6.5 w = 6.726812024 + 6.5 Combine like terms: 6.726812024 + 6.5 = 13.226812024 w = 13.226812024 Simplifying w = 13.226812024Subproblem 2
w + -6.5 = -6.726812024 Simplifying w + -6.5 = -6.726812024 Reorder the terms: -6.5 + w = -6.726812024 Solving -6.5 + w = -6.726812024 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + w = -6.726812024 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + w = -6.726812024 + 6.5 w = -6.726812024 + 6.5 Combine like terms: -6.726812024 + 6.5 = -0.226812024 w = -0.226812024 Simplifying w = -0.226812024Solution
The solution to the problem is based on the solutions from the subproblems. w = {13.226812024, -0.226812024}
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