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Simplifying 3w2 + -1 = 6w Reorder the terms: -1 + 3w2 = 6w Solving -1 + 3w2 = 6w Solving for variable 'w'. Reorder the terms: -1 + -6w + 3w2 = 6w + -6w Combine like terms: 6w + -6w = 0 -1 + -6w + 3w2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -0.3333333333 + -2w + w2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + -2w + 0.3333333333 + w2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + -2w + w2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + -2w + w2 = 0 + 0.3333333333 -2w + w2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 -2w + w2 = 0.3333333333 The w term is -2w. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2w + 1 + w2 = 0.3333333333 + 1 Reorder the terms: 1 + -2w + w2 = 0.3333333333 + 1 Combine like terms: 0.3333333333 + 1 = 1.3333333333 1 + -2w + w2 = 1.3333333333 Factor a perfect square on the left side: (w + -1)(w + -1) = 1.3333333333 Calculate the square root of the right side: 1.154700538 Break this problem into two subproblems by setting (w + -1) equal to 1.154700538 and -1.154700538.Subproblem 1
w + -1 = 1.154700538 Simplifying w + -1 = 1.154700538 Reorder the terms: -1 + w = 1.154700538 Solving -1 + w = 1.154700538 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + w = 1.154700538 + 1 Combine like terms: -1 + 1 = 0 0 + w = 1.154700538 + 1 w = 1.154700538 + 1 Combine like terms: 1.154700538 + 1 = 2.154700538 w = 2.154700538 Simplifying w = 2.154700538Subproblem 2
w + -1 = -1.154700538 Simplifying w + -1 = -1.154700538 Reorder the terms: -1 + w = -1.154700538 Solving -1 + w = -1.154700538 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + w = -1.154700538 + 1 Combine like terms: -1 + 1 = 0 0 + w = -1.154700538 + 1 w = -1.154700538 + 1 Combine like terms: -1.154700538 + 1 = -0.154700538 w = -0.154700538 Simplifying w = -0.154700538Solution
The solution to the problem is based on the solutions from the subproblems. w = {2.154700538, -0.154700538}
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