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Simplifying (w + -1)(3w + 2) = 4 Reorder the terms: (-1 + w)(3w + 2) = 4 Reorder the terms: (-1 + w)(2 + 3w) = 4 Multiply (-1 + w) * (2 + 3w) (-1(2 + 3w) + w(2 + 3w)) = 4 ((2 * -1 + 3w * -1) + w(2 + 3w)) = 4 ((-2 + -3w) + w(2 + 3w)) = 4 (-2 + -3w + (2 * w + 3w * w)) = 4 (-2 + -3w + (2w + 3w2)) = 4 Combine like terms: -3w + 2w = -1w (-2 + -1w + 3w2) = 4 Solving -2 + -1w + 3w2 = 4 Solving for variable 'w'. Reorder the terms: -2 + -4 + -1w + 3w2 = 4 + -4 Combine like terms: -2 + -4 = -6 -6 + -1w + 3w2 = 4 + -4 Combine like terms: 4 + -4 = 0 -6 + -1w + 3w2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2 + -0.3333333333w + w2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -0.3333333333w + 2 + w2 = 0 + 2 Reorder the terms: -2 + 2 + -0.3333333333w + w2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -0.3333333333w + w2 = 0 + 2 -0.3333333333w + w2 = 0 + 2 Combine like terms: 0 + 2 = 2 -0.3333333333w + w2 = 2 The w term is -0.3333333333w. Take half its coefficient (-0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. -0.3333333333w + 0.02777777779 + w2 = 2 + 0.02777777779 Reorder the terms: 0.02777777779 + -0.3333333333w + w2 = 2 + 0.02777777779 Combine like terms: 2 + 0.02777777779 = 2.02777777779 0.02777777779 + -0.3333333333w + w2 = 2.02777777779 Factor a perfect square on the left side: (w + -0.1666666667)(w + -0.1666666667) = 2.02777777779 Calculate the square root of the right side: 1.424000624 Break this problem into two subproblems by setting (w + -0.1666666667) equal to 1.424000624 and -1.424000624.Subproblem 1
w + -0.1666666667 = 1.424000624 Simplifying w + -0.1666666667 = 1.424000624 Reorder the terms: -0.1666666667 + w = 1.424000624 Solving -0.1666666667 + w = 1.424000624 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + w = 1.424000624 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + w = 1.424000624 + 0.1666666667 w = 1.424000624 + 0.1666666667 Combine like terms: 1.424000624 + 0.1666666667 = 1.5906672907 w = 1.5906672907 Simplifying w = 1.5906672907Subproblem 2
w + -0.1666666667 = -1.424000624 Simplifying w + -0.1666666667 = -1.424000624 Reorder the terms: -0.1666666667 + w = -1.424000624 Solving -0.1666666667 + w = -1.424000624 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + w = -1.424000624 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + w = -1.424000624 + 0.1666666667 w = -1.424000624 + 0.1666666667 Combine like terms: -1.424000624 + 0.1666666667 = -1.2573339573 w = -1.2573339573 Simplifying w = -1.2573339573Solution
The solution to the problem is based on the solutions from the subproblems. w = {1.5906672907, -1.2573339573}
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