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Simplifying w(w + 14) = 1976 Reorder the terms: w(14 + w) = 1976 (14 * w + w * w) = 1976 (14w + w2) = 1976 Solving 14w + w2 = 1976 Solving for variable 'w'. Reorder the terms: -1976 + 14w + w2 = 1976 + -1976 Combine like terms: 1976 + -1976 = 0 -1976 + 14w + w2 = 0 Factor a trinomial. (-52 + -1w)(38 + -1w) = 0Subproblem 1
Set the factor '(-52 + -1w)' equal to zero and attempt to solve: Simplifying -52 + -1w = 0 Solving -52 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '52' to each side of the equation. -52 + 52 + -1w = 0 + 52 Combine like terms: -52 + 52 = 0 0 + -1w = 0 + 52 -1w = 0 + 52 Combine like terms: 0 + 52 = 52 -1w = 52 Divide each side by '-1'. w = -52 Simplifying w = -52Subproblem 2
Set the factor '(38 + -1w)' equal to zero and attempt to solve: Simplifying 38 + -1w = 0 Solving 38 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-38' to each side of the equation. 38 + -38 + -1w = 0 + -38 Combine like terms: 38 + -38 = 0 0 + -1w = 0 + -38 -1w = 0 + -38 Combine like terms: 0 + -38 = -38 -1w = -38 Divide each side by '-1'. w = 38 Simplifying w = 38Solution
w = {-52, 38}
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