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Simplifying 2w2 + w = 5 Reorder the terms: w + 2w2 = 5 Solving w + 2w2 = 5 Solving for variable 'w'. Reorder the terms: -5 + w + 2w2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + w + 2w2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2.5 + 0.5w + w2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + 0.5w + 2.5 + w2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + 0.5w + w2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + 0.5w + w2 = 0 + 2.5 0.5w + w2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 0.5w + w2 = 2.5 The w term is w. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.5w + 0.25 + w2 = 2.5 + 0.25 Reorder the terms: 0.25 + 0.5w + w2 = 2.5 + 0.25 Combine like terms: 2.5 + 0.25 = 2.75 0.25 + 0.5w + w2 = 2.75 Factor a perfect square on the left side: (w + 0.5)(w + 0.5) = 2.75 Calculate the square root of the right side: 1.658312395 Break this problem into two subproblems by setting (w + 0.5) equal to 1.658312395 and -1.658312395.Subproblem 1
w + 0.5 = 1.658312395 Simplifying w + 0.5 = 1.658312395 Reorder the terms: 0.5 + w = 1.658312395 Solving 0.5 + w = 1.658312395 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + w = 1.658312395 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w = 1.658312395 + -0.5 w = 1.658312395 + -0.5 Combine like terms: 1.658312395 + -0.5 = 1.158312395 w = 1.158312395 Simplifying w = 1.158312395Subproblem 2
w + 0.5 = -1.658312395 Simplifying w + 0.5 = -1.658312395 Reorder the terms: 0.5 + w = -1.658312395 Solving 0.5 + w = -1.658312395 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + w = -1.658312395 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w = -1.658312395 + -0.5 w = -1.658312395 + -0.5 Combine like terms: -1.658312395 + -0.5 = -2.158312395 w = -2.158312395 Simplifying w = -2.158312395Solution
The solution to the problem is based on the solutions from the subproblems. w = {1.158312395, -2.158312395}
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