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Simplifying 5w2 + -22w + -200 = 0 Reorder the terms: -200 + -22w + 5w2 = 0 Solving -200 + -22w + 5w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -40 + -4.4w + w2 = 0 Move the constant term to the right: Add '40' to each side of the equation. -40 + -4.4w + 40 + w2 = 0 + 40 Reorder the terms: -40 + 40 + -4.4w + w2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + -4.4w + w2 = 0 + 40 -4.4w + w2 = 0 + 40 Combine like terms: 0 + 40 = 40 -4.4w + w2 = 40 The w term is -4.4w. Take half its coefficient (-2.2). Square it (4.84) and add it to both sides. Add '4.84' to each side of the equation. -4.4w + 4.84 + w2 = 40 + 4.84 Reorder the terms: 4.84 + -4.4w + w2 = 40 + 4.84 Combine like terms: 40 + 4.84 = 44.84 4.84 + -4.4w + w2 = 44.84 Factor a perfect square on the left side: (w + -2.2)(w + -2.2) = 44.84 Calculate the square root of the right side: 6.696267617 Break this problem into two subproblems by setting (w + -2.2) equal to 6.696267617 and -6.696267617.Subproblem 1
w + -2.2 = 6.696267617 Simplifying w + -2.2 = 6.696267617 Reorder the terms: -2.2 + w = 6.696267617 Solving -2.2 + w = 6.696267617 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2.2' to each side of the equation. -2.2 + 2.2 + w = 6.696267617 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + w = 6.696267617 + 2.2 w = 6.696267617 + 2.2 Combine like terms: 6.696267617 + 2.2 = 8.896267617 w = 8.896267617 Simplifying w = 8.896267617Subproblem 2
w + -2.2 = -6.696267617 Simplifying w + -2.2 = -6.696267617 Reorder the terms: -2.2 + w = -6.696267617 Solving -2.2 + w = -6.696267617 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2.2' to each side of the equation. -2.2 + 2.2 + w = -6.696267617 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + w = -6.696267617 + 2.2 w = -6.696267617 + 2.2 Combine like terms: -6.696267617 + 2.2 = -4.496267617 w = -4.496267617 Simplifying w = -4.496267617Solution
The solution to the problem is based on the solutions from the subproblems. w = {8.896267617, -4.496267617}
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