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Simplifying 2w2 + -5w + -22 = 0 Reorder the terms: -22 + -5w + 2w2 = 0 Solving -22 + -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'. -11 + -2.5w + w2 = 0 Move the constant term to the right: Add '11' to each side of the equation. -11 + -2.5w + 11 + w2 = 0 + 11 Reorder the terms: -11 + 11 + -2.5w + w2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -2.5w + w2 = 0 + 11 -2.5w + w2 = 0 + 11 Combine like terms: 0 + 11 = 11 -2.5w + w2 = 11 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 = 11 + 1.5625 Reorder the terms: 1.5625 + -2.5w + w2 = 11 + 1.5625 Combine like terms: 11 + 1.5625 = 12.5625 1.5625 + -2.5w + w2 = 12.5625 Factor a perfect square on the left side: (w + -1.25)(w + -1.25) = 12.5625 Calculate the square root of the right side: 3.54436172 Break this problem into two subproblems by setting (w + -1.25) equal to 3.54436172 and -3.54436172.Subproblem 1
w + -1.25 = 3.54436172 Simplifying w + -1.25 = 3.54436172 Reorder the terms: -1.25 + w = 3.54436172 Solving -1.25 + w = 3.54436172 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 = 3.54436172 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + w = 3.54436172 + 1.25 w = 3.54436172 + 1.25 Combine like terms: 3.54436172 + 1.25 = 4.79436172 w = 4.79436172 Simplifying w = 4.79436172Subproblem 2
w + -1.25 = -3.54436172 Simplifying w + -1.25 = -3.54436172 Reorder the terms: -1.25 + w = -3.54436172 Solving -1.25 + w = -3.54436172 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 = -3.54436172 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + w = -3.54436172 + 1.25 w = -3.54436172 + 1.25 Combine like terms: -3.54436172 + 1.25 = -2.29436172 w = -2.29436172 Simplifying w = -2.29436172Solution
The solution to the problem is based on the solutions from the subproblems. w = {4.79436172, -2.29436172}
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