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Simplifying 9w2 + -11 = 6w Reorder the terms: -11 + 9w2 = 6w Solving -11 + 9w2 = 6w Solving for variable 'w'. Reorder the terms: -11 + -6w + 9w2 = 6w + -6w Combine like terms: 6w + -6w = 0 -11 + -6w + 9w2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.222222222 + -0.6666666667w + w2 = 0 Move the constant term to the right: Add '1.222222222' to each side of the equation. -1.222222222 + -0.6666666667w + 1.222222222 + w2 = 0 + 1.222222222 Reorder the terms: -1.222222222 + 1.222222222 + -0.6666666667w + w2 = 0 + 1.222222222 Combine like terms: -1.222222222 + 1.222222222 = 0.000000000 0.000000000 + -0.6666666667w + w2 = 0 + 1.222222222 -0.6666666667w + w2 = 0 + 1.222222222 Combine like terms: 0 + 1.222222222 = 1.222222222 -0.6666666667w + w2 = 1.222222222 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 = 1.222222222 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667w + w2 = 1.222222222 + 0.1111111112 Combine like terms: 1.222222222 + 0.1111111112 = 1.3333333332 0.1111111112 + -0.6666666667w + w2 = 1.3333333332 Factor a perfect square on the left side: (w + -0.3333333334)(w + -0.3333333334) = 1.3333333332 Calculate the square root of the right side: 1.154700538 Break this problem into two subproblems by setting (w + -0.3333333334) equal to 1.154700538 and -1.154700538.Subproblem 1
w + -0.3333333334 = 1.154700538 Simplifying w + -0.3333333334 = 1.154700538 Reorder the terms: -0.3333333334 + w = 1.154700538 Solving -0.3333333334 + w = 1.154700538 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 = 1.154700538 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + w = 1.154700538 + 0.3333333334 w = 1.154700538 + 0.3333333334 Combine like terms: 1.154700538 + 0.3333333334 = 1.4880338714 w = 1.4880338714 Simplifying w = 1.4880338714Subproblem 2
w + -0.3333333334 = -1.154700538 Simplifying w + -0.3333333334 = -1.154700538 Reorder the terms: -0.3333333334 + w = -1.154700538 Solving -0.3333333334 + w = -1.154700538 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 = -1.154700538 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + w = -1.154700538 + 0.3333333334 w = -1.154700538 + 0.3333333334 Combine like terms: -1.154700538 + 0.3333333334 = -0.8213672046 w = -0.8213672046 Simplifying w = -0.8213672046Solution
The solution to the problem is based on the solutions from the subproblems. w = {1.4880338714, -0.8213672046}
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