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Simplifying 4w2 + -26w + 25 = 0 Reorder the terms: 25 + -26w + 4w2 = 0 Solving 25 + -26w + 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'. 6.25 + -6.5w + w2 = 0 Move the constant term to the right: Add '-6.25' to each side of the equation. 6.25 + -6.5w + -6.25 + w2 = 0 + -6.25 Reorder the terms: 6.25 + -6.25 + -6.5w + w2 = 0 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + -6.5w + w2 = 0 + -6.25 -6.5w + w2 = 0 + -6.25 Combine like terms: 0 + -6.25 = -6.25 -6.5w + w2 = -6.25 The w term is -6.5w. Take half its coefficient (-3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. -6.5w + 10.5625 + w2 = -6.25 + 10.5625 Reorder the terms: 10.5625 + -6.5w + w2 = -6.25 + 10.5625 Combine like terms: -6.25 + 10.5625 = 4.3125 10.5625 + -6.5w + w2 = 4.3125 Factor a perfect square on the left side: (w + -3.25)(w + -3.25) = 4.3125 Calculate the square root of the right side: 2.076655966 Break this problem into two subproblems by setting (w + -3.25) equal to 2.076655966 and -2.076655966.Subproblem 1
w + -3.25 = 2.076655966 Simplifying w + -3.25 = 2.076655966 Reorder the terms: -3.25 + w = 2.076655966 Solving -3.25 + w = 2.076655966 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + w = 2.076655966 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + w = 2.076655966 + 3.25 w = 2.076655966 + 3.25 Combine like terms: 2.076655966 + 3.25 = 5.326655966 w = 5.326655966 Simplifying w = 5.326655966Subproblem 2
w + -3.25 = -2.076655966 Simplifying w + -3.25 = -2.076655966 Reorder the terms: -3.25 + w = -2.076655966 Solving -3.25 + w = -2.076655966 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + w = -2.076655966 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + w = -2.076655966 + 3.25 w = -2.076655966 + 3.25 Combine like terms: -2.076655966 + 3.25 = 1.173344034 w = 1.173344034 Simplifying w = 1.173344034Solution
The solution to the problem is based on the solutions from the subproblems. w = {5.326655966, 1.173344034}
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