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Simplifying 2w2 + -4w + -6 + -2w + 1 = 0 Reorder the terms: -6 + 1 + -4w + -2w + 2w2 = 0 Combine like terms: -6 + 1 = -5 -5 + -4w + -2w + 2w2 = 0 Combine like terms: -4w + -2w = -6w -5 + -6w + 2w2 = 0 Solving -5 + -6w + 2w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2.5 + -3w + w2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -3w + 2.5 + w2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -3w + w2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -3w + w2 = 0 + 2.5 -3w + w2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -3w + w2 = 2.5 The w term is -3w. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3w + 2.25 + w2 = 2.5 + 2.25 Reorder the terms: 2.25 + -3w + w2 = 2.5 + 2.25 Combine like terms: 2.5 + 2.25 = 4.75 2.25 + -3w + w2 = 4.75 Factor a perfect square on the left side: (w + -1.5)(w + -1.5) = 4.75 Calculate the square root of the right side: 2.179449472 Break this problem into two subproblems by setting (w + -1.5) equal to 2.179449472 and -2.179449472.Subproblem 1
w + -1.5 = 2.179449472 Simplifying w + -1.5 = 2.179449472 Reorder the terms: -1.5 + w = 2.179449472 Solving -1.5 + w = 2.179449472 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + w = 2.179449472 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + w = 2.179449472 + 1.5 w = 2.179449472 + 1.5 Combine like terms: 2.179449472 + 1.5 = 3.679449472 w = 3.679449472 Simplifying w = 3.679449472Subproblem 2
w + -1.5 = -2.179449472 Simplifying w + -1.5 = -2.179449472 Reorder the terms: -1.5 + w = -2.179449472 Solving -1.5 + w = -2.179449472 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + w = -2.179449472 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + w = -2.179449472 + 1.5 w = -2.179449472 + 1.5 Combine like terms: -2.179449472 + 1.5 = -0.679449472 w = -0.679449472 Simplifying w = -0.679449472Solution
The solution to the problem is based on the solutions from the subproblems. w = {3.679449472, -0.679449472}
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