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Simplifying w2 + w = 5 Reorder the terms: w + w2 = 5 Solving w + w2 = 5 Solving for variable 'w'. Reorder the terms: -5 + w + w2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + w + 5 + w2 = 0 + 5 Reorder the terms: -5 + 5 + w + w2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + w + w2 = 0 + 5 w + w2 = 0 + 5 Combine like terms: 0 + 5 = 5 w + w2 = 5 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. w + 0.25 + w2 = 5 + 0.25 Reorder the terms: 0.25 + w + w2 = 5 + 0.25 Combine like terms: 5 + 0.25 = 5.25 0.25 + w + w2 = 5.25 Factor a perfect square on the left side: (w + 0.5)(w + 0.5) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (w + 0.5) equal to 2.291287847 and -2.291287847.Subproblem 1
w + 0.5 = 2.291287847 Simplifying w + 0.5 = 2.291287847 Reorder the terms: 0.5 + w = 2.291287847 Solving 0.5 + w = 2.291287847 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 = 2.291287847 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w = 2.291287847 + -0.5 w = 2.291287847 + -0.5 Combine like terms: 2.291287847 + -0.5 = 1.791287847 w = 1.791287847 Simplifying w = 1.791287847Subproblem 2
w + 0.5 = -2.291287847 Simplifying w + 0.5 = -2.291287847 Reorder the terms: 0.5 + w = -2.291287847 Solving 0.5 + w = -2.291287847 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 = -2.291287847 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w = -2.291287847 + -0.5 w = -2.291287847 + -0.5 Combine like terms: -2.291287847 + -0.5 = -2.791287847 w = -2.791287847 Simplifying w = -2.791287847Solution
The solution to the problem is based on the solutions from the subproblems. w = {1.791287847, -2.791287847}
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