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Simplifying 4w2 + -33w + -35 = 0 Reorder the terms: -35 + -33w + 4w2 = 0 Solving -35 + -33w + 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'. -8.75 + -8.25w + w2 = 0 Move the constant term to the right: Add '8.75' to each side of the equation. -8.75 + -8.25w + 8.75 + w2 = 0 + 8.75 Reorder the terms: -8.75 + 8.75 + -8.25w + w2 = 0 + 8.75 Combine like terms: -8.75 + 8.75 = 0.00 0.00 + -8.25w + w2 = 0 + 8.75 -8.25w + w2 = 0 + 8.75 Combine like terms: 0 + 8.75 = 8.75 -8.25w + w2 = 8.75 The w term is -8.25w. Take half its coefficient (-4.125). Square it (17.015625) and add it to both sides. Add '17.015625' to each side of the equation. -8.25w + 17.015625 + w2 = 8.75 + 17.015625 Reorder the terms: 17.015625 + -8.25w + w2 = 8.75 + 17.015625 Combine like terms: 8.75 + 17.015625 = 25.765625 17.015625 + -8.25w + w2 = 25.765625 Factor a perfect square on the left side: (w + -4.125)(w + -4.125) = 25.765625 Calculate the square root of the right side: 5.075985126 Break this problem into two subproblems by setting (w + -4.125) equal to 5.075985126 and -5.075985126.Subproblem 1
w + -4.125 = 5.075985126 Simplifying w + -4.125 = 5.075985126 Reorder the terms: -4.125 + w = 5.075985126 Solving -4.125 + w = 5.075985126 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '4.125' to each side of the equation. -4.125 + 4.125 + w = 5.075985126 + 4.125 Combine like terms: -4.125 + 4.125 = 0.000 0.000 + w = 5.075985126 + 4.125 w = 5.075985126 + 4.125 Combine like terms: 5.075985126 + 4.125 = 9.200985126 w = 9.200985126 Simplifying w = 9.200985126Subproblem 2
w + -4.125 = -5.075985126 Simplifying w + -4.125 = -5.075985126 Reorder the terms: -4.125 + w = -5.075985126 Solving -4.125 + w = -5.075985126 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '4.125' to each side of the equation. -4.125 + 4.125 + w = -5.075985126 + 4.125 Combine like terms: -4.125 + 4.125 = 0.000 0.000 + w = -5.075985126 + 4.125 w = -5.075985126 + 4.125 Combine like terms: -5.075985126 + 4.125 = -0.950985126 w = -0.950985126 Simplifying w = -0.950985126Solution
The solution to the problem is based on the solutions from the subproblems. w = {9.200985126, -0.950985126}
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