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Simplifying 2w2 + -5w + -154 = 0 Reorder the terms: -154 + -5w + 2w2 = 0 Solving -154 + -5w + 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'. -77 + -2.5w + w2 = 0 Move the constant term to the right: Add '77' to each side of the equation. -77 + -2.5w + 77 + w2 = 0 + 77 Reorder the terms: -77 + 77 + -2.5w + w2 = 0 + 77 Combine like terms: -77 + 77 = 0 0 + -2.5w + w2 = 0 + 77 -2.5w + w2 = 0 + 77 Combine like terms: 0 + 77 = 77 -2.5w + w2 = 77 The w term is -2.5w. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5w + 1.5625 + w2 = 77 + 1.5625 Reorder the terms: 1.5625 + -2.5w + w2 = 77 + 1.5625 Combine like terms: 77 + 1.5625 = 78.5625 1.5625 + -2.5w + w2 = 78.5625 Factor a perfect square on the left side: (w + -1.25)(w + -1.25) = 78.5625 Calculate the square root of the right side: 8.863548951 Break this problem into two subproblems by setting (w + -1.25) equal to 8.863548951 and -8.863548951.Subproblem 1
w + -1.25 = 8.863548951 Simplifying w + -1.25 = 8.863548951 Reorder the terms: -1.25 + w = 8.863548951 Solving -1.25 + w = 8.863548951 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + w = 8.863548951 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + w = 8.863548951 + 1.25 w = 8.863548951 + 1.25 Combine like terms: 8.863548951 + 1.25 = 10.113548951 w = 10.113548951 Simplifying w = 10.113548951Subproblem 2
w + -1.25 = -8.863548951 Simplifying w + -1.25 = -8.863548951 Reorder the terms: -1.25 + w = -8.863548951 Solving -1.25 + w = -8.863548951 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + w = -8.863548951 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + w = -8.863548951 + 1.25 w = -8.863548951 + 1.25 Combine like terms: -8.863548951 + 1.25 = -7.613548951 w = -7.613548951 Simplifying w = -7.613548951Solution
The solution to the problem is based on the solutions from the subproblems. w = {10.113548951, -7.613548951}
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