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Simplifying (1 + -1w)(4w + -7) = 0 Reorder the terms: (1 + -1w)(-7 + 4w) = 0 Multiply (1 + -1w) * (-7 + 4w) (1(-7 + 4w) + -1w * (-7 + 4w)) = 0 ((-7 * 1 + 4w * 1) + -1w * (-7 + 4w)) = 0 ((-7 + 4w) + -1w * (-7 + 4w)) = 0 (-7 + 4w + (-7 * -1w + 4w * -1w)) = 0 (-7 + 4w + (7w + -4w2)) = 0 Combine like terms: 4w + 7w = 11w (-7 + 11w + -4w2) = 0 Solving -7 + 11w + -4w2 = 0 Solving for variable 'w'. Factor a trinomial. (-7 + 4w)(1 + -1w) = 0Subproblem 1
Set the factor '(-7 + 4w)' equal to zero and attempt to solve: Simplifying -7 + 4w = 0 Solving -7 + 4w = 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 + 4w = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 4w = 0 + 7 4w = 0 + 7 Combine like terms: 0 + 7 = 7 4w = 7 Divide each side by '4'. w = 1.75 Simplifying w = 1.75Subproblem 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 = {1.75, 1}
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