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Simplifying 2w2 + -10w + 5 = 0 Reorder the terms: 5 + -10w + 2w2 = 0 Solving 5 + -10w + 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 + -5w + w2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + -5w + -2.5 + w2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + -5w + w2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + -5w + w2 = 0 + -2.5 -5w + w2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 -5w + w2 = -2.5 The w term is -5w. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5w + 6.25 + w2 = -2.5 + 6.25 Reorder the terms: 6.25 + -5w + w2 = -2.5 + 6.25 Combine like terms: -2.5 + 6.25 = 3.75 6.25 + -5w + w2 = 3.75 Factor a perfect square on the left side: (w + -2.5)(w + -2.5) = 3.75 Calculate the square root of the right side: 1.936491673 Break this problem into two subproblems by setting (w + -2.5) equal to 1.936491673 and -1.936491673.Subproblem 1
w + -2.5 = 1.936491673 Simplifying w + -2.5 = 1.936491673 Reorder the terms: -2.5 + w = 1.936491673 Solving -2.5 + w = 1.936491673 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + w = 1.936491673 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + w = 1.936491673 + 2.5 w = 1.936491673 + 2.5 Combine like terms: 1.936491673 + 2.5 = 4.436491673 w = 4.436491673 Simplifying w = 4.436491673Subproblem 2
w + -2.5 = -1.936491673 Simplifying w + -2.5 = -1.936491673 Reorder the terms: -2.5 + w = -1.936491673 Solving -2.5 + w = -1.936491673 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + w = -1.936491673 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + w = -1.936491673 + 2.5 w = -1.936491673 + 2.5 Combine like terms: -1.936491673 + 2.5 = 0.563508327 w = 0.563508327 Simplifying w = 0.563508327Solution
The solution to the problem is based on the solutions from the subproblems. w = {4.436491673, 0.563508327}
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