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Simplifying 4w2 + 21w + -5 = 0 Reorder the terms: -5 + 21w + 4w2 = 0 Solving -5 + 21w + 4w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.25 + 5.25w + w2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + 5.25w + 1.25 + w2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + 5.25w + w2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + 5.25w + w2 = 0 + 1.25 5.25w + w2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 5.25w + w2 = 1.25 The w term is 5.25w. Take half its coefficient (2.625). Square it (6.890625) and add it to both sides. Add '6.890625' to each side of the equation. 5.25w + 6.890625 + w2 = 1.25 + 6.890625 Reorder the terms: 6.890625 + 5.25w + w2 = 1.25 + 6.890625 Combine like terms: 1.25 + 6.890625 = 8.140625 6.890625 + 5.25w + w2 = 8.140625 Factor a perfect square on the left side: (w + 2.625)(w + 2.625) = 8.140625 Calculate the square root of the right side: 2.853178053 Break this problem into two subproblems by setting (w + 2.625) equal to 2.853178053 and -2.853178053.Subproblem 1
w + 2.625 = 2.853178053 Simplifying w + 2.625 = 2.853178053 Reorder the terms: 2.625 + w = 2.853178053 Solving 2.625 + w = 2.853178053 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2.625' to each side of the equation. 2.625 + -2.625 + w = 2.853178053 + -2.625 Combine like terms: 2.625 + -2.625 = 0.000 0.000 + w = 2.853178053 + -2.625 w = 2.853178053 + -2.625 Combine like terms: 2.853178053 + -2.625 = 0.228178053 w = 0.228178053 Simplifying w = 0.228178053Subproblem 2
w + 2.625 = -2.853178053 Simplifying w + 2.625 = -2.853178053 Reorder the terms: 2.625 + w = -2.853178053 Solving 2.625 + w = -2.853178053 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2.625' to each side of the equation. 2.625 + -2.625 + w = -2.853178053 + -2.625 Combine like terms: 2.625 + -2.625 = 0.000 0.000 + w = -2.853178053 + -2.625 w = -2.853178053 + -2.625 Combine like terms: -2.853178053 + -2.625 = -5.478178053 w = -5.478178053 Simplifying w = -5.478178053Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.228178053, -5.478178053}
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