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Simplifying -2w2 + 5w + 2 = 0 Reorder the terms: 2 + 5w + -2w2 = 0 Solving 2 + 5w + -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'. -1 + -2.5w + w2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -2.5w + 1 + w2 = 0 + 1 Reorder the terms: -1 + 1 + -2.5w + w2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2.5w + w2 = 0 + 1 -2.5w + w2 = 0 + 1 Combine like terms: 0 + 1 = 1 -2.5w + w2 = 1 The w term is -2.5w. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5w + 1.5625 + w2 = 1 + 1.5625 Reorder the terms: 1.5625 + -2.5w + w2 = 1 + 1.5625 Combine like terms: 1 + 1.5625 = 2.5625 1.5625 + -2.5w + w2 = 2.5625 Factor a perfect square on the left side: (w + -1.25)(w + -1.25) = 2.5625 Calculate the square root of the right side: 1.600781059 Break this problem into two subproblems by setting (w + -1.25) equal to 1.600781059 and -1.600781059.Subproblem 1
w + -1.25 = 1.600781059 Simplifying w + -1.25 = 1.600781059 Reorder the terms: -1.25 + w = 1.600781059 Solving -1.25 + w = 1.600781059 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + w = 1.600781059 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + w = 1.600781059 + 1.25 w = 1.600781059 + 1.25 Combine like terms: 1.600781059 + 1.25 = 2.850781059 w = 2.850781059 Simplifying w = 2.850781059Subproblem 2
w + -1.25 = -1.600781059 Simplifying w + -1.25 = -1.600781059 Reorder the terms: -1.25 + w = -1.600781059 Solving -1.25 + w = -1.600781059 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + w = -1.600781059 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + w = -1.600781059 + 1.25 w = -1.600781059 + 1.25 Combine like terms: -1.600781059 + 1.25 = -0.350781059 w = -0.350781059 Simplifying w = -0.350781059Solution
The solution to the problem is based on the solutions from the subproblems. w = {2.850781059, -0.350781059}
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