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Simplifying -3w2 + 2w + 12 = 0 Reorder the terms: 12 + 2w + -3w2 = 0 Solving 12 + 2w + -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'. -4 + -0.6666666667w + w2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -0.6666666667w + 4 + w2 = 0 + 4 Reorder the terms: -4 + 4 + -0.6666666667w + w2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -0.6666666667w + w2 = 0 + 4 -0.6666666667w + w2 = 0 + 4 Combine like terms: 0 + 4 = 4 -0.6666666667w + w2 = 4 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 = 4 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667w + w2 = 4 + 0.1111111112 Combine like terms: 4 + 0.1111111112 = 4.1111111112 0.1111111112 + -0.6666666667w + w2 = 4.1111111112 Factor a perfect square on the left side: (w + -0.3333333334)(w + -0.3333333334) = 4.1111111112 Calculate the square root of the right side: 2.02758751 Break this problem into two subproblems by setting (w + -0.3333333334) equal to 2.02758751 and -2.02758751.Subproblem 1
w + -0.3333333334 = 2.02758751 Simplifying w + -0.3333333334 = 2.02758751 Reorder the terms: -0.3333333334 + w = 2.02758751 Solving -0.3333333334 + w = 2.02758751 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 = 2.02758751 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + w = 2.02758751 + 0.3333333334 w = 2.02758751 + 0.3333333334 Combine like terms: 2.02758751 + 0.3333333334 = 2.3609208434 w = 2.3609208434 Simplifying w = 2.3609208434Subproblem 2
w + -0.3333333334 = -2.02758751 Simplifying w + -0.3333333334 = -2.02758751 Reorder the terms: -0.3333333334 + w = -2.02758751 Solving -0.3333333334 + w = -2.02758751 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 = -2.02758751 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + w = -2.02758751 + 0.3333333334 w = -2.02758751 + 0.3333333334 Combine like terms: -2.02758751 + 0.3333333334 = -1.6942541766 w = -1.6942541766 Simplifying w = -1.6942541766Solution
The solution to the problem is based on the solutions from the subproblems. w = {2.3609208434, -1.6942541766}
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