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Simplifying 14w2 + 7 = -21w Reorder the terms: 7 + 14w2 = -21w Solving 7 + 14w2 = -21w Solving for variable 'w'. Reorder the terms: 7 + 21w + 14w2 = -21w + 21w Combine like terms: -21w + 21w = 0 7 + 21w + 14w2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(1 + 3w + 2w2) = 0 Factor a trinomial. 7((1 + w)(1 + 2w)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(1 + w)' equal to zero and attempt to solve: Simplifying 1 + w = 0 Solving 1 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + w = 0 + -1 w = 0 + -1 Combine like terms: 0 + -1 = -1 w = -1 Simplifying w = -1Subproblem 2
Set the factor '(1 + 2w)' equal to zero and attempt to solve: Simplifying 1 + 2w = 0 Solving 1 + 2w = 0 Move all terms containing w to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2w = 0 + -1 2w = 0 + -1 Combine like terms: 0 + -1 = -1 2w = -1 Divide each side by '2'. w = -0.5 Simplifying w = -0.5Solution
w = {-1, -0.5}
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