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Simplifying 14w2 + -8w + 1 = -2w2 Reorder the terms: 1 + -8w + 14w2 = -2w2 Solving 1 + -8w + 14w2 = -2w2 Solving for variable 'w'. Combine like terms: 14w2 + 2w2 = 16w2 1 + -8w + 16w2 = -2w2 + 2w2 Combine like terms: -2w2 + 2w2 = 0 1 + -8w + 16w2 = 0 Factor a trinomial. (1 + -4w)(1 + -4w) = 0Subproblem 1
Set the factor '(1 + -4w)' equal to zero and attempt to solve: Simplifying 1 + -4w = 0 Solving 1 + -4w = 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 + -4w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4w = 0 + -1 -4w = 0 + -1 Combine like terms: 0 + -1 = -1 -4w = -1 Divide each side by '-4'. w = 0.25 Simplifying w = 0.25Subproblem 2
Set the factor '(1 + -4w)' equal to zero and attempt to solve: Simplifying 1 + -4w = 0 Solving 1 + -4w = 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 + -4w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4w = 0 + -1 -4w = 0 + -1 Combine like terms: 0 + -1 = -1 -4w = -1 Divide each side by '-4'. w = 0.25 Simplifying w = 0.25Solution
w = {0.25, 0.25}
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