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Simplifying -4w2 + w + 17 = 0 Reorder the terms: 17 + w + -4w2 = 0 Solving 17 + w + -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 + -0.25w + w2 = 0 Move the constant term to the right: Add '4.25' to each side of the equation. -4.25 + -0.25w + 4.25 + w2 = 0 + 4.25 Reorder the terms: -4.25 + 4.25 + -0.25w + w2 = 0 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + -0.25w + w2 = 0 + 4.25 -0.25w + w2 = 0 + 4.25 Combine like terms: 0 + 4.25 = 4.25 -0.25w + w2 = 4.25 The w term is w. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -0.25w + 0.25 + w2 = 4.25 + 0.25 Reorder the terms: 0.25 + -0.25w + w2 = 4.25 + 0.25 Combine like terms: 4.25 + 0.25 = 4.5 0.25 + -0.25w + w2 = 4.5 Factor a perfect square on the left side: (w + 0.5)(w + 0.5) = 4.5 Calculate the square root of the right side: 2.121320344 Break this problem into two subproblems by setting (w + 0.5) equal to 2.121320344 and -2.121320344.Subproblem 1
w + 0.5 = 2.121320344 Simplifying w + 0.5 = 2.121320344 Reorder the terms: 0.5 + w = 2.121320344 Solving 0.5 + w = 2.121320344 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + w = 2.121320344 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w = 2.121320344 + -0.5 w = 2.121320344 + -0.5 Combine like terms: 2.121320344 + -0.5 = 1.621320344 w = 1.621320344 Simplifying w = 1.621320344Subproblem 2
w + 0.5 = -2.121320344 Simplifying w + 0.5 = -2.121320344 Reorder the terms: 0.5 + w = -2.121320344 Solving 0.5 + w = -2.121320344 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + w = -2.121320344 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w = -2.121320344 + -0.5 w = -2.121320344 + -0.5 Combine like terms: -2.121320344 + -0.5 = -2.621320344 w = -2.621320344 Simplifying w = -2.621320344Solution
The solution to the problem is based on the solutions from the subproblems. w = {1.621320344, -2.621320344}
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