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Simplifying 0 = 5w2 + 18w + 10 Reorder the terms: 0 = 10 + 18w + 5w2 Solving 0 = 10 + 18w + 5w2 Solving for variable 'w'. Combine like terms: 0 + -10 = -10 -10 + -18w + -5w2 = 10 + 18w + 5w2 + -10 + -18w + -5w2 Reorder the terms: -10 + -18w + -5w2 = 10 + -10 + 18w + -18w + 5w2 + -5w2 Combine like terms: 10 + -10 = 0 -10 + -18w + -5w2 = 0 + 18w + -18w + 5w2 + -5w2 -10 + -18w + -5w2 = 18w + -18w + 5w2 + -5w2 Combine like terms: 18w + -18w = 0 -10 + -18w + -5w2 = 0 + 5w2 + -5w2 -10 + -18w + -5w2 = 5w2 + -5w2 Combine like terms: 5w2 + -5w2 = 0 -10 + -18w + -5w2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(10 + 18w + 5w2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(10 + 18w + 5w2)' equal to zero and attempt to solve: Simplifying 10 + 18w + 5w2 = 0 Solving 10 + 18w + 5w2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 2 + 3.6w + w2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + 3.6w + -2 + w2 = 0 + -2 Reorder the terms: 2 + -2 + 3.6w + w2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3.6w + w2 = 0 + -2 3.6w + w2 = 0 + -2 Combine like terms: 0 + -2 = -2 3.6w + w2 = -2 The w term is 3.6w. Take half its coefficient (1.8). Square it (3.24) and add it to both sides. Add '3.24' to each side of the equation. 3.6w + 3.24 + w2 = -2 + 3.24 Reorder the terms: 3.24 + 3.6w + w2 = -2 + 3.24 Combine like terms: -2 + 3.24 = 1.24 3.24 + 3.6w + w2 = 1.24 Factor a perfect square on the left side: (w + 1.8)(w + 1.8) = 1.24 Calculate the square root of the right side: 1.113552873 Break this problem into two subproblems by setting (w + 1.8) equal to 1.113552873 and -1.113552873.Subproblem 1
w + 1.8 = 1.113552873 Simplifying w + 1.8 = 1.113552873 Reorder the terms: 1.8 + w = 1.113552873 Solving 1.8 + w = 1.113552873 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.8' to each side of the equation. 1.8 + -1.8 + w = 1.113552873 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + w = 1.113552873 + -1.8 w = 1.113552873 + -1.8 Combine like terms: 1.113552873 + -1.8 = -0.686447127 w = -0.686447127 Simplifying w = -0.686447127Subproblem 2
w + 1.8 = -1.113552873 Simplifying w + 1.8 = -1.113552873 Reorder the terms: 1.8 + w = -1.113552873 Solving 1.8 + w = -1.113552873 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.8' to each side of the equation. 1.8 + -1.8 + w = -1.113552873 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + w = -1.113552873 + -1.8 w = -1.113552873 + -1.8 Combine like terms: -1.113552873 + -1.8 = -2.913552873 w = -2.913552873 Simplifying w = -2.913552873Solution
The solution to the problem is based on the solutions from the subproblems. w = {-0.686447127, -2.913552873}Solution
w = {-0.686447127, -2.913552873}
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