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Simplifying 2w2 + w + -42 = 0 Reorder the terms: -42 + w + 2w2 = 0 Solving -42 + w + 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'. -21 + 0.5w + w2 = 0 Move the constant term to the right: Add '21' to each side of the equation. -21 + 0.5w + 21 + w2 = 0 + 21 Reorder the terms: -21 + 21 + 0.5w + w2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + 0.5w + w2 = 0 + 21 0.5w + w2 = 0 + 21 Combine like terms: 0 + 21 = 21 0.5w + w2 = 21 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 = 21 + 0.25 Reorder the terms: 0.25 + 0.5w + w2 = 21 + 0.25 Combine like terms: 21 + 0.25 = 21.25 0.25 + 0.5w + w2 = 21.25 Factor a perfect square on the left side: (w + 0.5)(w + 0.5) = 21.25 Calculate the square root of the right side: 4.609772229 Break this problem into two subproblems by setting (w + 0.5) equal to 4.609772229 and -4.609772229.Subproblem 1
w + 0.5 = 4.609772229 Simplifying w + 0.5 = 4.609772229 Reorder the terms: 0.5 + w = 4.609772229 Solving 0.5 + w = 4.609772229 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 = 4.609772229 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w = 4.609772229 + -0.5 w = 4.609772229 + -0.5 Combine like terms: 4.609772229 + -0.5 = 4.109772229 w = 4.109772229 Simplifying w = 4.109772229Subproblem 2
w + 0.5 = -4.609772229 Simplifying w + 0.5 = -4.609772229 Reorder the terms: 0.5 + w = -4.609772229 Solving 0.5 + w = -4.609772229 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 = -4.609772229 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w = -4.609772229 + -0.5 w = -4.609772229 + -0.5 Combine like terms: -4.609772229 + -0.5 = -5.109772229 w = -5.109772229 Simplifying w = -5.109772229Solution
The solution to the problem is based on the solutions from the subproblems. w = {4.109772229, -5.109772229}
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