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Simplifying (2 + -1w)(2w + -7) = 0 Reorder the terms: (2 + -1w)(-7 + 2w) = 0 Multiply (2 + -1w) * (-7 + 2w) (2(-7 + 2w) + -1w * (-7 + 2w)) = 0 ((-7 * 2 + 2w * 2) + -1w * (-7 + 2w)) = 0 ((-14 + 4w) + -1w * (-7 + 2w)) = 0 (-14 + 4w + (-7 * -1w + 2w * -1w)) = 0 (-14 + 4w + (7w + -2w2)) = 0 Combine like terms: 4w + 7w = 11w (-14 + 11w + -2w2) = 0 Solving -14 + 11w + -2w2 = 0 Solving for variable 'w'. Factor a trinomial. (-7 + 2w)(2 + -1w) = 0Subproblem 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 '(2 + -1w)' equal to zero and attempt to solve: Simplifying 2 + -1w = 0 Solving 2 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1w = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1w = 0 + -2 -1w = 0 + -2 Combine like terms: 0 + -2 = -2 -1w = -2 Divide each side by '-1'. w = 2 Simplifying w = 2Solution
w = {3.5, 2}
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