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Simplifying 3w2 + -2w2 + -9w + 6 = 0 Reorder the terms: 6 + -9w + 3w2 + -2w2 = 0 Combine like terms: 3w2 + -2w2 = 1w2 6 + -9w + 1w2 = 0 Solving 6 + -9w + 1w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + -9w + -6 + w2 = 0 + -6 Reorder the terms: 6 + -6 + -9w + w2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -9w + w2 = 0 + -6 -9w + w2 = 0 + -6 Combine like terms: 0 + -6 = -6 -9w + w2 = -6 The w term is -9w. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9w + 20.25 + w2 = -6 + 20.25 Reorder the terms: 20.25 + -9w + w2 = -6 + 20.25 Combine like terms: -6 + 20.25 = 14.25 20.25 + -9w + w2 = 14.25 Factor a perfect square on the left side: (w + -4.5)(w + -4.5) = 14.25 Calculate the square root of the right side: 3.774917218 Break this problem into two subproblems by setting (w + -4.5) equal to 3.774917218 and -3.774917218.Subproblem 1
w + -4.5 = 3.774917218 Simplifying w + -4.5 = 3.774917218 Reorder the terms: -4.5 + w = 3.774917218 Solving -4.5 + w = 3.774917218 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + w = 3.774917218 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + w = 3.774917218 + 4.5 w = 3.774917218 + 4.5 Combine like terms: 3.774917218 + 4.5 = 8.274917218 w = 8.274917218 Simplifying w = 8.274917218Subproblem 2
w + -4.5 = -3.774917218 Simplifying w + -4.5 = -3.774917218 Reorder the terms: -4.5 + w = -3.774917218 Solving -4.5 + w = -3.774917218 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + w = -3.774917218 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + w = -3.774917218 + 4.5 w = -3.774917218 + 4.5 Combine like terms: -3.774917218 + 4.5 = 0.725082782 w = 0.725082782 Simplifying w = 0.725082782Solution
The solution to the problem is based on the solutions from the subproblems. w = {8.274917218, 0.725082782}
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