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Simplifying w2 + 10w + 25 = 0.25 Reorder the terms: 25 + 10w + w2 = 0.25 Solving 25 + 10w + w2 = 0.25 Solving for variable 'w'. Reorder the terms: 25 + -0.25 + 10w + w2 = 0.25 + -0.25 Combine like terms: 25 + -0.25 = 24.75 24.75 + 10w + w2 = 0.25 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 24.75 + 10w + w2 = 0.00 Begin completing the square. Move the constant term to the right: Add '-24.75' to each side of the equation. 24.75 + 10w + -24.75 + w2 = 0.00 + -24.75 Reorder the terms: 24.75 + -24.75 + 10w + w2 = 0.00 + -24.75 Combine like terms: 24.75 + -24.75 = 0.00 0.00 + 10w + w2 = 0.00 + -24.75 10w + w2 = 0.00 + -24.75 Combine like terms: 0.00 + -24.75 = -24.75 10w + w2 = -24.75 The w term is 10w. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10w + 25 + w2 = -24.75 + 25 Reorder the terms: 25 + 10w + w2 = -24.75 + 25 Combine like terms: -24.75 + 25 = 0.25 25 + 10w + w2 = 0.25 Factor a perfect square on the left side: (w + 5)(w + 5) = 0.25 Calculate the square root of the right side: 0.5 Break this problem into two subproblems by setting (w + 5) equal to 0.5 and -0.5.Subproblem 1
w + 5 = 0.5 Simplifying w + 5 = 0.5 Reorder the terms: 5 + w = 0.5 Solving 5 + w = 0.5 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + w = 0.5 + -5 Combine like terms: 5 + -5 = 0 0 + w = 0.5 + -5 w = 0.5 + -5 Combine like terms: 0.5 + -5 = -4.5 w = -4.5 Simplifying w = -4.5Subproblem 2
w + 5 = -0.5 Simplifying w + 5 = -0.5 Reorder the terms: 5 + w = -0.5 Solving 5 + w = -0.5 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + w = -0.5 + -5 Combine like terms: 5 + -5 = 0 0 + w = -0.5 + -5 w = -0.5 + -5 Combine like terms: -0.5 + -5 = -5.5 w = -5.5 Simplifying w = -5.5Solution
The solution to the problem is based on the solutions from the subproblems. w = {-4.5, -5.5}
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