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Simplifying 2w2 + 5w + -44 = 0 Reorder the terms: -44 + 5w + 2w2 = 0 Solving -44 + 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'. -22 + 2.5w + w2 = 0 Move the constant term to the right: Add '22' to each side of the equation. -22 + 2.5w + 22 + w2 = 0 + 22 Reorder the terms: -22 + 22 + 2.5w + w2 = 0 + 22 Combine like terms: -22 + 22 = 0 0 + 2.5w + w2 = 0 + 22 2.5w + w2 = 0 + 22 Combine like terms: 0 + 22 = 22 2.5w + w2 = 22 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 = 22 + 1.5625 Reorder the terms: 1.5625 + 2.5w + w2 = 22 + 1.5625 Combine like terms: 22 + 1.5625 = 23.5625 1.5625 + 2.5w + w2 = 23.5625 Factor a perfect square on the left side: (w + 1.25)(w + 1.25) = 23.5625 Calculate the square root of the right side: 4.85412196 Break this problem into two subproblems by setting (w + 1.25) equal to 4.85412196 and -4.85412196.Subproblem 1
w + 1.25 = 4.85412196 Simplifying w + 1.25 = 4.85412196 Reorder the terms: 1.25 + w = 4.85412196 Solving 1.25 + w = 4.85412196 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 = 4.85412196 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + w = 4.85412196 + -1.25 w = 4.85412196 + -1.25 Combine like terms: 4.85412196 + -1.25 = 3.60412196 w = 3.60412196 Simplifying w = 3.60412196Subproblem 2
w + 1.25 = -4.85412196 Simplifying w + 1.25 = -4.85412196 Reorder the terms: 1.25 + w = -4.85412196 Solving 1.25 + w = -4.85412196 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 = -4.85412196 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + w = -4.85412196 + -1.25 w = -4.85412196 + -1.25 Combine like terms: -4.85412196 + -1.25 = -6.10412196 w = -6.10412196 Simplifying w = -6.10412196Solution
The solution to the problem is based on the solutions from the subproblems. w = {3.60412196, -6.10412196}
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