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Simplifying 2w2 + 8w + -7 = 0 Reorder the terms: -7 + 8w + 2w2 = 0 Solving -7 + 8w + 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'. -3.5 + 4w + w2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + 4w + 3.5 + w2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + 4w + w2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + 4w + w2 = 0 + 3.5 4w + w2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 4w + w2 = 3.5 The w term is 4w. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4w + 4 + w2 = 3.5 + 4 Reorder the terms: 4 + 4w + w2 = 3.5 + 4 Combine like terms: 3.5 + 4 = 7.5 4 + 4w + w2 = 7.5 Factor a perfect square on the left side: (w + 2)(w + 2) = 7.5 Calculate the square root of the right side: 2.738612788 Break this problem into two subproblems by setting (w + 2) equal to 2.738612788 and -2.738612788.Subproblem 1
w + 2 = 2.738612788 Simplifying w + 2 = 2.738612788 Reorder the terms: 2 + w = 2.738612788 Solving 2 + w = 2.738612788 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + w = 2.738612788 + -2 Combine like terms: 2 + -2 = 0 0 + w = 2.738612788 + -2 w = 2.738612788 + -2 Combine like terms: 2.738612788 + -2 = 0.738612788 w = 0.738612788 Simplifying w = 0.738612788Subproblem 2
w + 2 = -2.738612788 Simplifying w + 2 = -2.738612788 Reorder the terms: 2 + w = -2.738612788 Solving 2 + w = -2.738612788 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + w = -2.738612788 + -2 Combine like terms: 2 + -2 = 0 0 + w = -2.738612788 + -2 w = -2.738612788 + -2 Combine like terms: -2.738612788 + -2 = -4.738612788 w = -4.738612788 Simplifying w = -4.738612788Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.738612788, -4.738612788}
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