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Simplifying 0 = -4w2 + -27w + 18 Reorder the terms: 0 = 18 + -27w + -4w2 Solving 0 = 18 + -27w + -4w2 Solving for variable 'w'. Combine like terms: 0 + -18 = -18 -18 + 27w + 4w2 = 18 + -27w + -4w2 + -18 + 27w + 4w2 Reorder the terms: -18 + 27w + 4w2 = 18 + -18 + -27w + 27w + -4w2 + 4w2 Combine like terms: 18 + -18 = 0 -18 + 27w + 4w2 = 0 + -27w + 27w + -4w2 + 4w2 -18 + 27w + 4w2 = -27w + 27w + -4w2 + 4w2 Combine like terms: -27w + 27w = 0 -18 + 27w + 4w2 = 0 + -4w2 + 4w2 -18 + 27w + 4w2 = -4w2 + 4w2 Combine like terms: -4w2 + 4w2 = 0 -18 + 27w + 4w2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -4.5 + 6.75w + w2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + 6.75w + 4.5 + w2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + 6.75w + w2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + 6.75w + w2 = 0 + 4.5 6.75w + w2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 6.75w + w2 = 4.5 The w term is 6.75w. Take half its coefficient (3.375). Square it (11.390625) and add it to both sides. Add '11.390625' to each side of the equation. 6.75w + 11.390625 + w2 = 4.5 + 11.390625 Reorder the terms: 11.390625 + 6.75w + w2 = 4.5 + 11.390625 Combine like terms: 4.5 + 11.390625 = 15.890625 11.390625 + 6.75w + w2 = 15.890625 Factor a perfect square on the left side: (w + 3.375)(w + 3.375) = 15.890625 Calculate the square root of the right side: 3.98630468 Break this problem into two subproblems by setting (w + 3.375) equal to 3.98630468 and -3.98630468.Subproblem 1
w + 3.375 = 3.98630468 Simplifying w + 3.375 = 3.98630468 Reorder the terms: 3.375 + w = 3.98630468 Solving 3.375 + w = 3.98630468 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3.375' to each side of the equation. 3.375 + -3.375 + w = 3.98630468 + -3.375 Combine like terms: 3.375 + -3.375 = 0.000 0.000 + w = 3.98630468 + -3.375 w = 3.98630468 + -3.375 Combine like terms: 3.98630468 + -3.375 = 0.61130468 w = 0.61130468 Simplifying w = 0.61130468Subproblem 2
w + 3.375 = -3.98630468 Simplifying w + 3.375 = -3.98630468 Reorder the terms: 3.375 + w = -3.98630468 Solving 3.375 + w = -3.98630468 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3.375' to each side of the equation. 3.375 + -3.375 + w = -3.98630468 + -3.375 Combine like terms: 3.375 + -3.375 = 0.000 0.000 + w = -3.98630468 + -3.375 w = -3.98630468 + -3.375 Combine like terms: -3.98630468 + -3.375 = -7.36130468 w = -7.36130468 Simplifying w = -7.36130468Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.61130468, -7.36130468}
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