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Simplifying w(w + 12) = 253 Reorder the terms: w(12 + w) = 253 (12 * w + w * w) = 253 (12w + w2) = 253 Solving 12w + w2 = 253 Solving for variable 'w'. Reorder the terms: -253 + 12w + w2 = 253 + -253 Combine like terms: 253 + -253 = 0 -253 + 12w + w2 = 0 Factor a trinomial. (-23 + -1w)(11 + -1w) = 0Subproblem 1
Set the factor '(-23 + -1w)' equal to zero and attempt to solve: Simplifying -23 + -1w = 0 Solving -23 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '23' to each side of the equation. -23 + 23 + -1w = 0 + 23 Combine like terms: -23 + 23 = 0 0 + -1w = 0 + 23 -1w = 0 + 23 Combine like terms: 0 + 23 = 23 -1w = 23 Divide each side by '-1'. w = -23 Simplifying w = -23Subproblem 2
Set the factor '(11 + -1w)' equal to zero and attempt to solve: Simplifying 11 + -1w = 0 Solving 11 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -1w = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -1w = 0 + -11 -1w = 0 + -11 Combine like terms: 0 + -11 = -11 -1w = -11 Divide each side by '-1'. w = 11 Simplifying w = 11Solution
w = {-23, 11}
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