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Simplifying 3w + 21 + -4w2 = 0 Reorder the terms: 21 + 3w + -4w2 = 0 Solving 21 + 3w + -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'. -5.25 + -0.75w + w2 = 0 Move the constant term to the right: Add '5.25' to each side of the equation. -5.25 + -0.75w + 5.25 + w2 = 0 + 5.25 Reorder the terms: -5.25 + 5.25 + -0.75w + w2 = 0 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + -0.75w + w2 = 0 + 5.25 -0.75w + w2 = 0 + 5.25 Combine like terms: 0 + 5.25 = 5.25 -0.75w + w2 = 5.25 The w term is -0.75w. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75w + 0.140625 + w2 = 5.25 + 0.140625 Reorder the terms: 0.140625 + -0.75w + w2 = 5.25 + 0.140625 Combine like terms: 5.25 + 0.140625 = 5.390625 0.140625 + -0.75w + w2 = 5.390625 Factor a perfect square on the left side: (w + -0.375)(w + -0.375) = 5.390625 Calculate the square root of the right side: 2.321771953 Break this problem into two subproblems by setting (w + -0.375) equal to 2.321771953 and -2.321771953.Subproblem 1
w + -0.375 = 2.321771953 Simplifying w + -0.375 = 2.321771953 Reorder the terms: -0.375 + w = 2.321771953 Solving -0.375 + w = 2.321771953 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + w = 2.321771953 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + w = 2.321771953 + 0.375 w = 2.321771953 + 0.375 Combine like terms: 2.321771953 + 0.375 = 2.696771953 w = 2.696771953 Simplifying w = 2.696771953Subproblem 2
w + -0.375 = -2.321771953 Simplifying w + -0.375 = -2.321771953 Reorder the terms: -0.375 + w = -2.321771953 Solving -0.375 + w = -2.321771953 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + w = -2.321771953 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + w = -2.321771953 + 0.375 w = -2.321771953 + 0.375 Combine like terms: -2.321771953 + 0.375 = -1.946771953 w = -1.946771953 Simplifying w = -1.946771953Solution
The solution to the problem is based on the solutions from the subproblems. w = {2.696771953, -1.946771953}
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