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Simplifying (2w2) + 60w + -175 = 0 Reorder the terms: -175 + 60w + (2w2) = 0 Solving -175 + 60w + (2w2) = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -87.5 + 30w + w2 = 0 Move the constant term to the right: Add '87.5' to each side of the equation. -87.5 + 30w + 87.5 + w2 = 0 + 87.5 Reorder the terms: -87.5 + 87.5 + 30w + w2 = 0 + 87.5 Combine like terms: -87.5 + 87.5 = 0.0 0.0 + 30w + w2 = 0 + 87.5 30w + w2 = 0 + 87.5 Combine like terms: 0 + 87.5 = 87.5 30w + w2 = 87.5 The w term is 30w. Take half its coefficient (15). Square it (225) and add it to both sides. Add '225' to each side of the equation. 30w + 225 + w2 = 87.5 + 225 Reorder the terms: 225 + 30w + w2 = 87.5 + 225 Combine like terms: 87.5 + 225 = 312.5 225 + 30w + w2 = 312.5 Factor a perfect square on the left side: ((w) + 15)((w) + 15) = 312.5 Calculate the square root of the right side: 17.67766953 Break this problem into two subproblems by setting ((w) + 15) equal to 17.67766953 and -17.67766953.Subproblem 1
(w) + 15 = 17.67766953 Simplifying (w) + 15 = 17.67766953 w + 15 = 17.67766953 Reorder the terms: 15 + w = 17.67766953 Solving 15 + w = 17.67766953 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + w = 17.67766953 + -15 Combine like terms: 15 + -15 = 0 0 + w = 17.67766953 + -15 w = 17.67766953 + -15 Combine like terms: 17.67766953 + -15 = 2.67766953 w = 2.67766953 Simplifying w = 2.67766953Subproblem 2
(w) + 15 = -17.67766953 Simplifying (w) + 15 = -17.67766953 w + 15 = -17.67766953 Reorder the terms: 15 + w = -17.67766953 Solving 15 + w = -17.67766953 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + w = -17.67766953 + -15 Combine like terms: 15 + -15 = 0 0 + w = -17.67766953 + -15 w = -17.67766953 + -15 Combine like terms: -17.67766953 + -15 = -32.67766953 w = -32.67766953 Simplifying w = -32.67766953Solution
The solution to the problem is based on the solutions from the subproblems. w = {2.67766953, -32.67766953}
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