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Simplifying 560 = 8w(w + 3) Reorder the terms: 560 = 8w(3 + w) 560 = (3 * 8w + w * 8w) 560 = (24w + 8w2) Solving 560 = 24w + 8w2 Solving for variable 'w'. Reorder the terms: 560 + -24w + -8w2 = 24w + -24w + 8w2 + -8w2 Combine like terms: 24w + -24w = 0 560 + -24w + -8w2 = 0 + 8w2 + -8w2 560 + -24w + -8w2 = 8w2 + -8w2 Combine like terms: 8w2 + -8w2 = 0 560 + -24w + -8w2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(70 + -3w + -1w2) = 0 Factor a trinomial. 8((7 + -1w)(10 + w)) = 0 Ignore the factor 8.Subproblem 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 '(10 + w)' equal to zero and attempt to solve: Simplifying 10 + w = 0 Solving 10 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + w = 0 + -10 Combine like terms: 10 + -10 = 0 0 + w = 0 + -10 w = 0 + -10 Combine like terms: 0 + -10 = -10 w = -10 Simplifying w = -10Solution
w = {7, -10}
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