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Simplifying 4w(4w + 4) + 2w = 7(w + 8) + -29 Reorder the terms: 4w(4 + 4w) + 2w = 7(w + 8) + -29 (4 * 4w + 4w * 4w) + 2w = 7(w + 8) + -29 (16w + 16w2) + 2w = 7(w + 8) + -29 Reorder the terms: 16w + 2w + 16w2 = 7(w + 8) + -29 Combine like terms: 16w + 2w = 18w 18w + 16w2 = 7(w + 8) + -29 Reorder the terms: 18w + 16w2 = 7(8 + w) + -29 18w + 16w2 = (8 * 7 + w * 7) + -29 18w + 16w2 = (56 + 7w) + -29 Reorder the terms: 18w + 16w2 = 56 + -29 + 7w Combine like terms: 56 + -29 = 27 18w + 16w2 = 27 + 7w Solving 18w + 16w2 = 27 + 7w Solving for variable 'w'. Reorder the terms: -27 + 18w + -7w + 16w2 = 27 + 7w + -27 + -7w Combine like terms: 18w + -7w = 11w -27 + 11w + 16w2 = 27 + 7w + -27 + -7w Reorder the terms: -27 + 11w + 16w2 = 27 + -27 + 7w + -7w Combine like terms: 27 + -27 = 0 -27 + 11w + 16w2 = 0 + 7w + -7w -27 + 11w + 16w2 = 7w + -7w Combine like terms: 7w + -7w = 0 -27 + 11w + 16w2 = 0 Factor a trinomial. (-27 + -16w)(1 + -1w) = 0Subproblem 1
Set the factor '(-27 + -16w)' equal to zero and attempt to solve: Simplifying -27 + -16w = 0 Solving -27 + -16w = 0 Move all terms containing w to the left, all other terms to the right. Add '27' to each side of the equation. -27 + 27 + -16w = 0 + 27 Combine like terms: -27 + 27 = 0 0 + -16w = 0 + 27 -16w = 0 + 27 Combine like terms: 0 + 27 = 27 -16w = 27 Divide each side by '-16'. w = -1.6875 Simplifying w = -1.6875Subproblem 2
Set the factor '(1 + -1w)' equal to zero and attempt to solve: Simplifying 1 + -1w = 0 Solving 1 + -1w = 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 + -1w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1w = 0 + -1 -1w = 0 + -1 Combine like terms: 0 + -1 = -1 -1w = -1 Divide each side by '-1'. w = 1 Simplifying w = 1Solution
w = {-1.6875, 1}
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