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Simplifying w + w2 = 70 Solving w + w2 = 70 Solving for variable 'w'. Reorder the terms: -70 + w + w2 = 70 + -70 Combine like terms: 70 + -70 = 0 -70 + w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '70' to each side of the equation. -70 + w + 70 + w2 = 0 + 70 Reorder the terms: -70 + 70 + w + w2 = 0 + 70 Combine like terms: -70 + 70 = 0 0 + w + w2 = 0 + 70 w + w2 = 0 + 70 Combine like terms: 0 + 70 = 70 w + w2 = 70 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 = 70 + 0.25 Reorder the terms: 0.25 + w + w2 = 70 + 0.25 Combine like terms: 70 + 0.25 = 70.25 0.25 + w + w2 = 70.25 Factor a perfect square on the left side: (w + 0.5)(w + 0.5) = 70.25 Calculate the square root of the right side: 8.381527307 Break this problem into two subproblems by setting (w + 0.5) equal to 8.381527307 and -8.381527307.Subproblem 1
w + 0.5 = 8.381527307 Simplifying w + 0.5 = 8.381527307 Reorder the terms: 0.5 + w = 8.381527307 Solving 0.5 + w = 8.381527307 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 = 8.381527307 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w = 8.381527307 + -0.5 w = 8.381527307 + -0.5 Combine like terms: 8.381527307 + -0.5 = 7.881527307 w = 7.881527307 Simplifying w = 7.881527307Subproblem 2
w + 0.5 = -8.381527307 Simplifying w + 0.5 = -8.381527307 Reorder the terms: 0.5 + w = -8.381527307 Solving 0.5 + w = -8.381527307 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 = -8.381527307 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w = -8.381527307 + -0.5 w = -8.381527307 + -0.5 Combine like terms: -8.381527307 + -0.5 = -8.881527307 w = -8.881527307 Simplifying w = -8.881527307Solution
The solution to the problem is based on the solutions from the subproblems. w = {7.881527307, -8.881527307}
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