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Simplifying (-1w2 + -5w + 6) + (-2w2 + 4) = 0 Reorder the terms: (6 + -5w + -1w2) + (-2w2 + 4) = 0 Remove parenthesis around (6 + -5w + -1w2) 6 + -5w + -1w2 + (-2w2 + 4) = 0 Reorder the terms: 6 + -5w + -1w2 + (4 + -2w2) = 0 Remove parenthesis around (4 + -2w2) 6 + -5w + -1w2 + 4 + -2w2 = 0 Reorder the terms: 6 + 4 + -5w + -1w2 + -2w2 = 0 Combine like terms: 6 + 4 = 10 10 + -5w + -1w2 + -2w2 = 0 Combine like terms: -1w2 + -2w2 = -3w2 10 + -5w + -3w2 = 0 Solving 10 + -5w + -3w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -3.333333333 + 1.666666667w + w2 = 0 Move the constant term to the right: Add '3.333333333' to each side of the equation. -3.333333333 + 1.666666667w + 3.333333333 + w2 = 0 + 3.333333333 Reorder the terms: -3.333333333 + 3.333333333 + 1.666666667w + w2 = 0 + 3.333333333 Combine like terms: -3.333333333 + 3.333333333 = 0.000000000 0.000000000 + 1.666666667w + w2 = 0 + 3.333333333 1.666666667w + w2 = 0 + 3.333333333 Combine like terms: 0 + 3.333333333 = 3.333333333 1.666666667w + w2 = 3.333333333 The w term is 1.666666667w. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667w + 0.6944444447 + w2 = 3.333333333 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667w + w2 = 3.333333333 + 0.6944444447 Combine like terms: 3.333333333 + 0.6944444447 = 4.0277777777 0.6944444447 + 1.666666667w + w2 = 4.0277777777 Factor a perfect square on the left side: (w + 0.8333333335)(w + 0.8333333335) = 4.0277777777 Calculate the square root of the right side: 2.00693243 Break this problem into two subproblems by setting (w + 0.8333333335) equal to 2.00693243 and -2.00693243.Subproblem 1
w + 0.8333333335 = 2.00693243 Simplifying w + 0.8333333335 = 2.00693243 Reorder the terms: 0.8333333335 + w = 2.00693243 Solving 0.8333333335 + w = 2.00693243 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + w = 2.00693243 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + w = 2.00693243 + -0.8333333335 w = 2.00693243 + -0.8333333335 Combine like terms: 2.00693243 + -0.8333333335 = 1.1735990965 w = 1.1735990965 Simplifying w = 1.1735990965Subproblem 2
w + 0.8333333335 = -2.00693243 Simplifying w + 0.8333333335 = -2.00693243 Reorder the terms: 0.8333333335 + w = -2.00693243 Solving 0.8333333335 + w = -2.00693243 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + w = -2.00693243 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + w = -2.00693243 + -0.8333333335 w = -2.00693243 + -0.8333333335 Combine like terms: -2.00693243 + -0.8333333335 = -2.8402657635 w = -2.8402657635 Simplifying w = -2.8402657635Solution
The solution to the problem is based on the solutions from the subproblems. w = {1.1735990965, -2.8402657635}
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