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Simplifying w2 + 5w + -20 = 0 Reorder the terms: -20 + 5w + w2 = 0 Solving -20 + 5w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + 5w + 20 + w2 = 0 + 20 Reorder the terms: -20 + 20 + 5w + w2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 5w + w2 = 0 + 20 5w + w2 = 0 + 20 Combine like terms: 0 + 20 = 20 5w + w2 = 20 The w term is 5w. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5w + 6.25 + w2 = 20 + 6.25 Reorder the terms: 6.25 + 5w + w2 = 20 + 6.25 Combine like terms: 20 + 6.25 = 26.25 6.25 + 5w + w2 = 26.25 Factor a perfect square on the left side: (w + 2.5)(w + 2.5) = 26.25 Calculate the square root of the right side: 5.123475383 Break this problem into two subproblems by setting (w + 2.5) equal to 5.123475383 and -5.123475383.Subproblem 1
w + 2.5 = 5.123475383 Simplifying w + 2.5 = 5.123475383 Reorder the terms: 2.5 + w = 5.123475383 Solving 2.5 + w = 5.123475383 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + w = 5.123475383 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + w = 5.123475383 + -2.5 w = 5.123475383 + -2.5 Combine like terms: 5.123475383 + -2.5 = 2.623475383 w = 2.623475383 Simplifying w = 2.623475383Subproblem 2
w + 2.5 = -5.123475383 Simplifying w + 2.5 = -5.123475383 Reorder the terms: 2.5 + w = -5.123475383 Solving 2.5 + w = -5.123475383 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + w = -5.123475383 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + w = -5.123475383 + -2.5 w = -5.123475383 + -2.5 Combine like terms: -5.123475383 + -2.5 = -7.623475383 w = -7.623475383 Simplifying w = -7.623475383Solution
The solution to the problem is based on the solutions from the subproblems. w = {2.623475383, -7.623475383}
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