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Simplifying w2 = 5w + 3 Reorder the terms: w2 = 3 + 5w Solving w2 = 3 + 5w Solving for variable 'w'. Reorder the terms: -3 + -5w + w2 = 3 + 5w + -3 + -5w Reorder the terms: -3 + -5w + w2 = 3 + -3 + 5w + -5w Combine like terms: 3 + -3 = 0 -3 + -5w + w2 = 0 + 5w + -5w -3 + -5w + w2 = 5w + -5w Combine like terms: 5w + -5w = 0 -3 + -5w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -5w + 3 + w2 = 0 + 3 Reorder the terms: -3 + 3 + -5w + w2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -5w + w2 = 0 + 3 -5w + w2 = 0 + 3 Combine like terms: 0 + 3 = 3 -5w + w2 = 3 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 = 3 + 6.25 Reorder the terms: 6.25 + -5w + w2 = 3 + 6.25 Combine like terms: 3 + 6.25 = 9.25 6.25 + -5w + w2 = 9.25 Factor a perfect square on the left side: (w + -2.5)(w + -2.5) = 9.25 Calculate the square root of the right side: 3.041381265 Break this problem into two subproblems by setting (w + -2.5) equal to 3.041381265 and -3.041381265.Subproblem 1
w + -2.5 = 3.041381265 Simplifying w + -2.5 = 3.041381265 Reorder the terms: -2.5 + w = 3.041381265 Solving -2.5 + w = 3.041381265 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 = 3.041381265 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + w = 3.041381265 + 2.5 w = 3.041381265 + 2.5 Combine like terms: 3.041381265 + 2.5 = 5.541381265 w = 5.541381265 Simplifying w = 5.541381265Subproblem 2
w + -2.5 = -3.041381265 Simplifying w + -2.5 = -3.041381265 Reorder the terms: -2.5 + w = -3.041381265 Solving -2.5 + w = -3.041381265 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 = -3.041381265 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + w = -3.041381265 + 2.5 w = -3.041381265 + 2.5 Combine like terms: -3.041381265 + 2.5 = -0.541381265 w = -0.541381265 Simplifying w = -0.541381265Solution
The solution to the problem is based on the solutions from the subproblems. w = {5.541381265, -0.541381265}
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