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Simplifying 175 + 60w + 4w2 = 0 Solving 175 + 60w + 4w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 43.75 + 15w + w2 = 0 Move the constant term to the right: Add '-43.75' to each side of the equation. 43.75 + 15w + -43.75 + w2 = 0 + -43.75 Reorder the terms: 43.75 + -43.75 + 15w + w2 = 0 + -43.75 Combine like terms: 43.75 + -43.75 = 0.00 0.00 + 15w + w2 = 0 + -43.75 15w + w2 = 0 + -43.75 Combine like terms: 0 + -43.75 = -43.75 15w + w2 = -43.75 The w term is 15w. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15w + 56.25 + w2 = -43.75 + 56.25 Reorder the terms: 56.25 + 15w + w2 = -43.75 + 56.25 Combine like terms: -43.75 + 56.25 = 12.5 56.25 + 15w + w2 = 12.5 Factor a perfect square on the left side: (w + 7.5)(w + 7.5) = 12.5 Calculate the square root of the right side: 3.535533906 Break this problem into two subproblems by setting (w + 7.5) equal to 3.535533906 and -3.535533906.Subproblem 1
w + 7.5 = 3.535533906 Simplifying w + 7.5 = 3.535533906 Reorder the terms: 7.5 + w = 3.535533906 Solving 7.5 + w = 3.535533906 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + w = 3.535533906 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + w = 3.535533906 + -7.5 w = 3.535533906 + -7.5 Combine like terms: 3.535533906 + -7.5 = -3.964466094 w = -3.964466094 Simplifying w = -3.964466094Subproblem 2
w + 7.5 = -3.535533906 Simplifying w + 7.5 = -3.535533906 Reorder the terms: 7.5 + w = -3.535533906 Solving 7.5 + w = -3.535533906 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + w = -3.535533906 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + w = -3.535533906 + -7.5 w = -3.535533906 + -7.5 Combine like terms: -3.535533906 + -7.5 = -11.035533906 w = -11.035533906 Simplifying w = -11.035533906Solution
The solution to the problem is based on the solutions from the subproblems. w = {-3.964466094, -11.035533906}
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