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Simplifying 4w2 + 31w + -33 = 0 Reorder the terms: -33 + 31w + 4w2 = 0 Solving -33 + 31w + 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'. -8.25 + 7.75w + w2 = 0 Move the constant term to the right: Add '8.25' to each side of the equation. -8.25 + 7.75w + 8.25 + w2 = 0 + 8.25 Reorder the terms: -8.25 + 8.25 + 7.75w + w2 = 0 + 8.25 Combine like terms: -8.25 + 8.25 = 0.00 0.00 + 7.75w + w2 = 0 + 8.25 7.75w + w2 = 0 + 8.25 Combine like terms: 0 + 8.25 = 8.25 7.75w + w2 = 8.25 The w term is 7.75w. Take half its coefficient (3.875). Square it (15.015625) and add it to both sides. Add '15.015625' to each side of the equation. 7.75w + 15.015625 + w2 = 8.25 + 15.015625 Reorder the terms: 15.015625 + 7.75w + w2 = 8.25 + 15.015625 Combine like terms: 8.25 + 15.015625 = 23.265625 15.015625 + 7.75w + w2 = 23.265625 Factor a perfect square on the left side: (w + 3.875)(w + 3.875) = 23.265625 Calculate the square root of the right side: 4.823445345 Break this problem into two subproblems by setting (w + 3.875) equal to 4.823445345 and -4.823445345.Subproblem 1
w + 3.875 = 4.823445345 Simplifying w + 3.875 = 4.823445345 Reorder the terms: 3.875 + w = 4.823445345 Solving 3.875 + w = 4.823445345 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3.875' to each side of the equation. 3.875 + -3.875 + w = 4.823445345 + -3.875 Combine like terms: 3.875 + -3.875 = 0.000 0.000 + w = 4.823445345 + -3.875 w = 4.823445345 + -3.875 Combine like terms: 4.823445345 + -3.875 = 0.948445345 w = 0.948445345 Simplifying w = 0.948445345Subproblem 2
w + 3.875 = -4.823445345 Simplifying w + 3.875 = -4.823445345 Reorder the terms: 3.875 + w = -4.823445345 Solving 3.875 + w = -4.823445345 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3.875' to each side of the equation. 3.875 + -3.875 + w = -4.823445345 + -3.875 Combine like terms: 3.875 + -3.875 = 0.000 0.000 + w = -4.823445345 + -3.875 w = -4.823445345 + -3.875 Combine like terms: -4.823445345 + -3.875 = -8.698445345 w = -8.698445345 Simplifying w = -8.698445345Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.948445345, -8.698445345}
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