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Simplifying 9w2 + -2w + -57 = 0 Reorder the terms: -57 + -2w + 9w2 = 0 Solving -57 + -2w + 9w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -6.333333333 + -0.2222222222w + w2 = 0 Move the constant term to the right: Add '6.333333333' to each side of the equation. -6.333333333 + -0.2222222222w + 6.333333333 + w2 = 0 + 6.333333333 Reorder the terms: -6.333333333 + 6.333333333 + -0.2222222222w + w2 = 0 + 6.333333333 Combine like terms: -6.333333333 + 6.333333333 = 0.000000000 0.000000000 + -0.2222222222w + w2 = 0 + 6.333333333 -0.2222222222w + w2 = 0 + 6.333333333 Combine like terms: 0 + 6.333333333 = 6.333333333 -0.2222222222w + w2 = 6.333333333 The w term is -0.2222222222w. Take half its coefficient (-0.1111111111). Square it (0.01234567901) and add it to both sides. Add '0.01234567901' to each side of the equation. -0.2222222222w + 0.01234567901 + w2 = 6.333333333 + 0.01234567901 Reorder the terms: 0.01234567901 + -0.2222222222w + w2 = 6.333333333 + 0.01234567901 Combine like terms: 6.333333333 + 0.01234567901 = 6.34567901201 0.01234567901 + -0.2222222222w + w2 = 6.34567901201 Factor a perfect square on the left side: (w + -0.1111111111)(w + -0.1111111111) = 6.34567901201 Calculate the square root of the right side: 2.519063122 Break this problem into two subproblems by setting (w + -0.1111111111) equal to 2.519063122 and -2.519063122.Subproblem 1
w + -0.1111111111 = 2.519063122 Simplifying w + -0.1111111111 = 2.519063122 Reorder the terms: -0.1111111111 + w = 2.519063122 Solving -0.1111111111 + w = 2.519063122 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.1111111111' to each side of the equation. -0.1111111111 + 0.1111111111 + w = 2.519063122 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + w = 2.519063122 + 0.1111111111 w = 2.519063122 + 0.1111111111 Combine like terms: 2.519063122 + 0.1111111111 = 2.6301742331 w = 2.6301742331 Simplifying w = 2.6301742331Subproblem 2
w + -0.1111111111 = -2.519063122 Simplifying w + -0.1111111111 = -2.519063122 Reorder the terms: -0.1111111111 + w = -2.519063122 Solving -0.1111111111 + w = -2.519063122 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.1111111111' to each side of the equation. -0.1111111111 + 0.1111111111 + w = -2.519063122 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + w = -2.519063122 + 0.1111111111 w = -2.519063122 + 0.1111111111 Combine like terms: -2.519063122 + 0.1111111111 = -2.4079520109 w = -2.4079520109 Simplifying w = -2.4079520109Solution
The solution to the problem is based on the solutions from the subproblems. w = {2.6301742331, -2.4079520109}
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