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Simplifying 2w2 + 8w + -81 = 0 Reorder the terms: -81 + 8w + 2w2 = 0 Solving -81 + 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'. -40.5 + 4w + w2 = 0 Move the constant term to the right: Add '40.5' to each side of the equation. -40.5 + 4w + 40.5 + w2 = 0 + 40.5 Reorder the terms: -40.5 + 40.5 + 4w + w2 = 0 + 40.5 Combine like terms: -40.5 + 40.5 = 0.0 0.0 + 4w + w2 = 0 + 40.5 4w + w2 = 0 + 40.5 Combine like terms: 0 + 40.5 = 40.5 4w + w2 = 40.5 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 = 40.5 + 4 Reorder the terms: 4 + 4w + w2 = 40.5 + 4 Combine like terms: 40.5 + 4 = 44.5 4 + 4w + w2 = 44.5 Factor a perfect square on the left side: (w + 2)(w + 2) = 44.5 Calculate the square root of the right side: 6.670832032 Break this problem into two subproblems by setting (w + 2) equal to 6.670832032 and -6.670832032.Subproblem 1
w + 2 = 6.670832032 Simplifying w + 2 = 6.670832032 Reorder the terms: 2 + w = 6.670832032 Solving 2 + w = 6.670832032 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 = 6.670832032 + -2 Combine like terms: 2 + -2 = 0 0 + w = 6.670832032 + -2 w = 6.670832032 + -2 Combine like terms: 6.670832032 + -2 = 4.670832032 w = 4.670832032 Simplifying w = 4.670832032Subproblem 2
w + 2 = -6.670832032 Simplifying w + 2 = -6.670832032 Reorder the terms: 2 + w = -6.670832032 Solving 2 + w = -6.670832032 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 = -6.670832032 + -2 Combine like terms: 2 + -2 = 0 0 + w = -6.670832032 + -2 w = -6.670832032 + -2 Combine like terms: -6.670832032 + -2 = -8.670832032 w = -8.670832032 Simplifying w = -8.670832032Solution
The solution to the problem is based on the solutions from the subproblems. w = {4.670832032, -8.670832032}
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