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Simplifying w + 4 = w2 + 6w + -11 Reorder the terms: 4 + w = w2 + 6w + -11 Reorder the terms: 4 + w = -11 + 6w + w2 Solving 4 + w = -11 + 6w + w2 Solving for variable 'w'. Reorder the terms: 4 + 11 + w + -6w + -1w2 = -11 + 6w + w2 + 11 + -6w + -1w2 Combine like terms: 4 + 11 = 15 15 + w + -6w + -1w2 = -11 + 6w + w2 + 11 + -6w + -1w2 Combine like terms: w + -6w = -5w 15 + -5w + -1w2 = -11 + 6w + w2 + 11 + -6w + -1w2 Reorder the terms: 15 + -5w + -1w2 = -11 + 11 + 6w + -6w + w2 + -1w2 Combine like terms: -11 + 11 = 0 15 + -5w + -1w2 = 0 + 6w + -6w + w2 + -1w2 15 + -5w + -1w2 = 6w + -6w + w2 + -1w2 Combine like terms: 6w + -6w = 0 15 + -5w + -1w2 = 0 + w2 + -1w2 15 + -5w + -1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 15 + -5w + -1w2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -15 + 5w + w2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + 5w + 15 + w2 = 0 + 15 Reorder the terms: -15 + 15 + 5w + w2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 5w + w2 = 0 + 15 5w + w2 = 0 + 15 Combine like terms: 0 + 15 = 15 5w + w2 = 15 The w term is 5w. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5w + 6.25 + w2 = 15 + 6.25 Reorder the terms: 6.25 + 5w + w2 = 15 + 6.25 Combine like terms: 15 + 6.25 = 21.25 6.25 + 5w + w2 = 21.25 Factor a perfect square on the left side: (w + 2.5)(w + 2.5) = 21.25 Calculate the square root of the right side: 4.609772229 Break this problem into two subproblems by setting (w + 2.5) equal to 4.609772229 and -4.609772229.Subproblem 1
w + 2.5 = 4.609772229 Simplifying w + 2.5 = 4.609772229 Reorder the terms: 2.5 + w = 4.609772229 Solving 2.5 + w = 4.609772229 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + w = 4.609772229 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + w = 4.609772229 + -2.5 w = 4.609772229 + -2.5 Combine like terms: 4.609772229 + -2.5 = 2.109772229 w = 2.109772229 Simplifying w = 2.109772229Subproblem 2
w + 2.5 = -4.609772229 Simplifying w + 2.5 = -4.609772229 Reorder the terms: 2.5 + w = -4.609772229 Solving 2.5 + w = -4.609772229 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + w = -4.609772229 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + w = -4.609772229 + -2.5 w = -4.609772229 + -2.5 Combine like terms: -4.609772229 + -2.5 = -7.109772229 w = -7.109772229 Simplifying w = -7.109772229Solution
The solution to the problem is based on the solutions from the subproblems. w = {2.109772229, -7.109772229}
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