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Simplifying 4w2 + -24w + 17 = 0 Reorder the terms: 17 + -24w + 4w2 = 0 Solving 17 + -24w + 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'. 4.25 + -6w + w2 = 0 Move the constant term to the right: Add '-4.25' to each side of the equation. 4.25 + -6w + -4.25 + w2 = 0 + -4.25 Reorder the terms: 4.25 + -4.25 + -6w + w2 = 0 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + -6w + w2 = 0 + -4.25 -6w + w2 = 0 + -4.25 Combine like terms: 0 + -4.25 = -4.25 -6w + w2 = -4.25 The w term is -6w. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6w + 9 + w2 = -4.25 + 9 Reorder the terms: 9 + -6w + w2 = -4.25 + 9 Combine like terms: -4.25 + 9 = 4.75 9 + -6w + w2 = 4.75 Factor a perfect square on the left side: (w + -3)(w + -3) = 4.75 Calculate the square root of the right side: 2.179449472 Break this problem into two subproblems by setting (w + -3) equal to 2.179449472 and -2.179449472.Subproblem 1
w + -3 = 2.179449472 Simplifying w + -3 = 2.179449472 Reorder the terms: -3 + w = 2.179449472 Solving -3 + w = 2.179449472 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + w = 2.179449472 + 3 Combine like terms: -3 + 3 = 0 0 + w = 2.179449472 + 3 w = 2.179449472 + 3 Combine like terms: 2.179449472 + 3 = 5.179449472 w = 5.179449472 Simplifying w = 5.179449472Subproblem 2
w + -3 = -2.179449472 Simplifying w + -3 = -2.179449472 Reorder the terms: -3 + w = -2.179449472 Solving -3 + w = -2.179449472 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + w = -2.179449472 + 3 Combine like terms: -3 + 3 = 0 0 + w = -2.179449472 + 3 w = -2.179449472 + 3 Combine like terms: -2.179449472 + 3 = 0.820550528 w = 0.820550528 Simplifying w = 0.820550528Solution
The solution to the problem is based on the solutions from the subproblems. w = {5.179449472, 0.820550528}
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