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Simplifying (-3w2 + 6w + -4) + (2w2 + 7w + 5) = 0 Reorder the terms: (-4 + 6w + -3w2) + (2w2 + 7w + 5) = 0 Remove parenthesis around (-4 + 6w + -3w2) -4 + 6w + -3w2 + (2w2 + 7w + 5) = 0 Reorder the terms: -4 + 6w + -3w2 + (5 + 7w + 2w2) = 0 Remove parenthesis around (5 + 7w + 2w2) -4 + 6w + -3w2 + 5 + 7w + 2w2 = 0 Reorder the terms: -4 + 5 + 6w + 7w + -3w2 + 2w2 = 0 Combine like terms: -4 + 5 = 1 1 + 6w + 7w + -3w2 + 2w2 = 0 Combine like terms: 6w + 7w = 13w 1 + 13w + -3w2 + 2w2 = 0 Combine like terms: -3w2 + 2w2 = -1w2 1 + 13w + -1w2 = 0 Solving 1 + 13w + -1w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1 + -13w + w2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -13w + 1 + w2 = 0 + 1 Reorder the terms: -1 + 1 + -13w + w2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -13w + w2 = 0 + 1 -13w + w2 = 0 + 1 Combine like terms: 0 + 1 = 1 -13w + w2 = 1 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 = 1 + 42.25 Reorder the terms: 42.25 + -13w + w2 = 1 + 42.25 Combine like terms: 1 + 42.25 = 43.25 42.25 + -13w + w2 = 43.25 Factor a perfect square on the left side: (w + -6.5)(w + -6.5) = 43.25 Calculate the square root of the right side: 6.576473219 Break this problem into two subproblems by setting (w + -6.5) equal to 6.576473219 and -6.576473219.Subproblem 1
w + -6.5 = 6.576473219 Simplifying w + -6.5 = 6.576473219 Reorder the terms: -6.5 + w = 6.576473219 Solving -6.5 + w = 6.576473219 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 = 6.576473219 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + w = 6.576473219 + 6.5 w = 6.576473219 + 6.5 Combine like terms: 6.576473219 + 6.5 = 13.076473219 w = 13.076473219 Simplifying w = 13.076473219Subproblem 2
w + -6.5 = -6.576473219 Simplifying w + -6.5 = -6.576473219 Reorder the terms: -6.5 + w = -6.576473219 Solving -6.5 + w = -6.576473219 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 = -6.576473219 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + w = -6.576473219 + 6.5 w = -6.576473219 + 6.5 Combine like terms: -6.576473219 + 6.5 = -0.076473219 w = -0.076473219 Simplifying w = -0.076473219Solution
The solution to the problem is based on the solutions from the subproblems. w = {13.076473219, -0.076473219}
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