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Simplifying w(3w + -2) = 36 Reorder the terms: w(-2 + 3w) = 36 (-2 * w + 3w * w) = 36 (-2w + 3w2) = 36 Solving -2w + 3w2 = 36 Solving for variable 'w'. Reorder the terms: -36 + -2w + 3w2 = 36 + -36 Combine like terms: 36 + -36 = 0 -36 + -2w + 3w2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -12 + -0.6666666667w + w2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + -0.6666666667w + 12 + w2 = 0 + 12 Reorder the terms: -12 + 12 + -0.6666666667w + w2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -0.6666666667w + w2 = 0 + 12 -0.6666666667w + w2 = 0 + 12 Combine like terms: 0 + 12 = 12 -0.6666666667w + w2 = 12 The w term is -0.6666666667w. Take half its coefficient (-0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. -0.6666666667w + 0.1111111112 + w2 = 12 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667w + w2 = 12 + 0.1111111112 Combine like terms: 12 + 0.1111111112 = 12.1111111112 0.1111111112 + -0.6666666667w + w2 = 12.1111111112 Factor a perfect square on the left side: (w + -0.3333333334)(w + -0.3333333334) = 12.1111111112 Calculate the square root of the right side: 3.48010217 Break this problem into two subproblems by setting (w + -0.3333333334) equal to 3.48010217 and -3.48010217.Subproblem 1
w + -0.3333333334 = 3.48010217 Simplifying w + -0.3333333334 = 3.48010217 Reorder the terms: -0.3333333334 + w = 3.48010217 Solving -0.3333333334 + w = 3.48010217 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + w = 3.48010217 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + w = 3.48010217 + 0.3333333334 w = 3.48010217 + 0.3333333334 Combine like terms: 3.48010217 + 0.3333333334 = 3.8134355034 w = 3.8134355034 Simplifying w = 3.8134355034Subproblem 2
w + -0.3333333334 = -3.48010217 Simplifying w + -0.3333333334 = -3.48010217 Reorder the terms: -0.3333333334 + w = -3.48010217 Solving -0.3333333334 + w = -3.48010217 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + w = -3.48010217 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + w = -3.48010217 + 0.3333333334 w = -3.48010217 + 0.3333333334 Combine like terms: -3.48010217 + 0.3333333334 = -3.1467688366 w = -3.1467688366 Simplifying w = -3.1467688366Solution
The solution to the problem is based on the solutions from the subproblems. w = {3.8134355034, -3.1467688366}
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