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Simplifying 4w2 + -7w + 1 = 0 Reorder the terms: 1 + -7w + 4w2 = 0 Solving 1 + -7w + 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'. 0.25 + -1.75w + w2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + -1.75w + -0.25 + w2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + -1.75w + w2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + -1.75w + w2 = 0 + -0.25 -1.75w + w2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 -1.75w + w2 = -0.25 The w term is -1.75w. Take half its coefficient (-0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. -1.75w + 0.765625 + w2 = -0.25 + 0.765625 Reorder the terms: 0.765625 + -1.75w + w2 = -0.25 + 0.765625 Combine like terms: -0.25 + 0.765625 = 0.515625 0.765625 + -1.75w + w2 = 0.515625 Factor a perfect square on the left side: (w + -0.875)(w + -0.875) = 0.515625 Calculate the square root of the right side: 0.718070331 Break this problem into two subproblems by setting (w + -0.875) equal to 0.718070331 and -0.718070331.Subproblem 1
w + -0.875 = 0.718070331 Simplifying w + -0.875 = 0.718070331 Reorder the terms: -0.875 + w = 0.718070331 Solving -0.875 + w = 0.718070331 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + w = 0.718070331 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + w = 0.718070331 + 0.875 w = 0.718070331 + 0.875 Combine like terms: 0.718070331 + 0.875 = 1.593070331 w = 1.593070331 Simplifying w = 1.593070331Subproblem 2
w + -0.875 = -0.718070331 Simplifying w + -0.875 = -0.718070331 Reorder the terms: -0.875 + w = -0.718070331 Solving -0.875 + w = -0.718070331 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + w = -0.718070331 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + w = -0.718070331 + 0.875 w = -0.718070331 + 0.875 Combine like terms: -0.718070331 + 0.875 = 0.156929669 w = 0.156929669 Simplifying w = 0.156929669Solution
The solution to the problem is based on the solutions from the subproblems. w = {1.593070331, 0.156929669}
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