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Simplifying w(w + 3) * 28 = 3640 Reorder the terms: w(3 + w) * 28 = 3640 Reorder the terms for easier multiplication: 28w(3 + w) = 3640 (3 * 28w + w * 28w) = 3640 (84w + 28w2) = 3640 Solving 84w + 28w2 = 3640 Solving for variable 'w'. Reorder the terms: -3640 + 84w + 28w2 = 3640 + -3640 Combine like terms: 3640 + -3640 = 0 -3640 + 84w + 28w2 = 0 Factor out the Greatest Common Factor (GCF), '28'. 28(-130 + 3w + w2) = 0 Factor a trinomial. 28((-13 + -1w)(10 + -1w)) = 0 Ignore the factor 28.Subproblem 1
Set the factor '(-13 + -1w)' equal to zero and attempt to solve: Simplifying -13 + -1w = 0 Solving -13 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + -1w = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -1w = 0 + 13 -1w = 0 + 13 Combine like terms: 0 + 13 = 13 -1w = 13 Divide each side by '-1'. w = -13 Simplifying w = -13Subproblem 2
Set the factor '(10 + -1w)' equal to zero and attempt to solve: Simplifying 10 + -1w = 0 Solving 10 + -1w = 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 + -1w = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1w = 0 + -10 -1w = 0 + -10 Combine like terms: 0 + -10 = -10 -1w = -10 Divide each side by '-1'. w = 10 Simplifying w = 10Solution
w = {-13, 10}
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