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Simplifying (-6w2 + 4w + -3) + (7w2 + 2w + 1) = 0 Reorder the terms: (-3 + 4w + -6w2) + (7w2 + 2w + 1) = 0 Remove parenthesis around (-3 + 4w + -6w2) -3 + 4w + -6w2 + (7w2 + 2w + 1) = 0 Reorder the terms: -3 + 4w + -6w2 + (1 + 2w + 7w2) = 0 Remove parenthesis around (1 + 2w + 7w2) -3 + 4w + -6w2 + 1 + 2w + 7w2 = 0 Reorder the terms: -3 + 1 + 4w + 2w + -6w2 + 7w2 = 0 Combine like terms: -3 + 1 = -2 -2 + 4w + 2w + -6w2 + 7w2 = 0 Combine like terms: 4w + 2w = 6w -2 + 6w + -6w2 + 7w2 = 0 Combine like terms: -6w2 + 7w2 = 1w2 -2 + 6w + 1w2 = 0 Solving -2 + 6w + 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 + 6w + 2 + w2 = 0 + 2 Reorder the terms: -2 + 2 + 6w + w2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 6w + w2 = 0 + 2 6w + w2 = 0 + 2 Combine like terms: 0 + 2 = 2 6w + w2 = 2 The w term is 6w. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6w + 9 + w2 = 2 + 9 Reorder the terms: 9 + 6w + w2 = 2 + 9 Combine like terms: 2 + 9 = 11 9 + 6w + w2 = 11 Factor a perfect square on the left side: (w + 3)(w + 3) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (w + 3) equal to 3.31662479 and -3.31662479.Subproblem 1
w + 3 = 3.31662479 Simplifying w + 3 = 3.31662479 Reorder the terms: 3 + w = 3.31662479 Solving 3 + w = 3.31662479 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + w = 3.31662479 + -3 Combine like terms: 3 + -3 = 0 0 + w = 3.31662479 + -3 w = 3.31662479 + -3 Combine like terms: 3.31662479 + -3 = 0.31662479 w = 0.31662479 Simplifying w = 0.31662479Subproblem 2
w + 3 = -3.31662479 Simplifying w + 3 = -3.31662479 Reorder the terms: 3 + w = -3.31662479 Solving 3 + w = -3.31662479 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + w = -3.31662479 + -3 Combine like terms: 3 + -3 = 0 0 + w = -3.31662479 + -3 w = -3.31662479 + -3 Combine like terms: -3.31662479 + -3 = -6.31662479 w = -6.31662479 Simplifying w = -6.31662479Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.31662479, -6.31662479}
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