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Simplifying 24w2 + 168w + 294 = 0 Reorder the terms: 294 + 168w + 24w2 = 0 Solving 294 + 168w + 24w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '6'. 6(49 + 28w + 4w2) = 0 Factor a trinomial. 6((7 + 2w)(7 + 2w)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(7 + 2w)' equal to zero and attempt to solve: Simplifying 7 + 2w = 0 Solving 7 + 2w = 0 Move all terms containing w to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 2w = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 2w = 0 + -7 2w = 0 + -7 Combine like terms: 0 + -7 = -7 2w = -7 Divide each side by '2'. w = -3.5 Simplifying w = -3.5Subproblem 2
Set the factor '(7 + 2w)' equal to zero and attempt to solve: Simplifying 7 + 2w = 0 Solving 7 + 2w = 0 Move all terms containing w to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 2w = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 2w = 0 + -7 2w = 0 + -7 Combine like terms: 0 + -7 = -7 2w = -7 Divide each side by '2'. w = -3.5 Simplifying w = -3.5Solution
w = {-3.5, -3.5}
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