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Simplifying 0 = 5w2 + 18w + 12 Reorder the terms: 0 = 12 + 18w + 5w2 Solving 0 = 12 + 18w + 5w2 Solving for variable 'w'. Combine like terms: 0 + -12 = -12 -12 + -18w + -5w2 = 12 + 18w + 5w2 + -12 + -18w + -5w2 Reorder the terms: -12 + -18w + -5w2 = 12 + -12 + 18w + -18w + 5w2 + -5w2 Combine like terms: 12 + -12 = 0 -12 + -18w + -5w2 = 0 + 18w + -18w + 5w2 + -5w2 -12 + -18w + -5w2 = 18w + -18w + 5w2 + -5w2 Combine like terms: 18w + -18w = 0 -12 + -18w + -5w2 = 0 + 5w2 + -5w2 -12 + -18w + -5w2 = 5w2 + -5w2 Combine like terms: 5w2 + -5w2 = 0 -12 + -18w + -5w2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(12 + 18w + 5w2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(12 + 18w + 5w2)' equal to zero and attempt to solve: Simplifying 12 + 18w + 5w2 = 0 Solving 12 + 18w + 5w2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 2.4 + 3.6w + w2 = 0 Move the constant term to the right: Add '-2.4' to each side of the equation. 2.4 + 3.6w + -2.4 + w2 = 0 + -2.4 Reorder the terms: 2.4 + -2.4 + 3.6w + w2 = 0 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + 3.6w + w2 = 0 + -2.4 3.6w + w2 = 0 + -2.4 Combine like terms: 0 + -2.4 = -2.4 3.6w + w2 = -2.4 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 = -2.4 + 3.24 Reorder the terms: 3.24 + 3.6w + w2 = -2.4 + 3.24 Combine like terms: -2.4 + 3.24 = 0.84 3.24 + 3.6w + w2 = 0.84 Factor a perfect square on the left side: (w + 1.8)(w + 1.8) = 0.84 Calculate the square root of the right side: 0.916515139 Break this problem into two subproblems by setting (w + 1.8) equal to 0.916515139 and -0.916515139.Subproblem 1
w + 1.8 = 0.916515139 Simplifying w + 1.8 = 0.916515139 Reorder the terms: 1.8 + w = 0.916515139 Solving 1.8 + w = 0.916515139 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 = 0.916515139 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + w = 0.916515139 + -1.8 w = 0.916515139 + -1.8 Combine like terms: 0.916515139 + -1.8 = -0.883484861 w = -0.883484861 Simplifying w = -0.883484861Subproblem 2
w + 1.8 = -0.916515139 Simplifying w + 1.8 = -0.916515139 Reorder the terms: 1.8 + w = -0.916515139 Solving 1.8 + w = -0.916515139 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 = -0.916515139 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + w = -0.916515139 + -1.8 w = -0.916515139 + -1.8 Combine like terms: -0.916515139 + -1.8 = -2.716515139 w = -2.716515139 Simplifying w = -2.716515139Solution
The solution to the problem is based on the solutions from the subproblems. w = {-0.883484861, -2.716515139}Solution
w = {-0.883484861, -2.716515139}
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