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Simplifying 7 = w(w + -6) Reorder the terms: 7 = w(-6 + w) 7 = (-6 * w + w * w) 7 = (-6w + w2) Solving 7 = -6w + w2 Solving for variable 'w'. Reorder the terms: 7 + 6w + -1w2 = -6w + 6w + w2 + -1w2 Combine like terms: -6w + 6w = 0 7 + 6w + -1w2 = 0 + w2 + -1w2 7 + 6w + -1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 7 + 6w + -1w2 = 0 Factor a trinomial. (7 + -1w)(1 + w) = 0Subproblem 1
Set the factor '(7 + -1w)' equal to zero and attempt to solve: Simplifying 7 + -1w = 0 Solving 7 + -1w = 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 + -1w = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1w = 0 + -7 -1w = 0 + -7 Combine like terms: 0 + -7 = -7 -1w = -7 Divide each side by '-1'. w = 7 Simplifying w = 7Subproblem 2
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 = -1Solution
w = {7, -1}
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