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Simplifying 0 = 225 + -50w + w2 Solving 0 = 225 + -50w + w2 Solving for variable 'w'. Combine like terms: 0 + -225 = -225 -225 + 50w + -1w2 = 225 + -50w + w2 + -225 + 50w + -1w2 Reorder the terms: -225 + 50w + -1w2 = 225 + -225 + -50w + 50w + w2 + -1w2 Combine like terms: 225 + -225 = 0 -225 + 50w + -1w2 = 0 + -50w + 50w + w2 + -1w2 -225 + 50w + -1w2 = -50w + 50w + w2 + -1w2 Combine like terms: -50w + 50w = 0 -225 + 50w + -1w2 = 0 + w2 + -1w2 -225 + 50w + -1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 -225 + 50w + -1w2 = 0 Factor a trinomial. (-45 + w)(5 + -1w) = 0Subproblem 1
Set the factor '(-45 + w)' equal to zero and attempt to solve: Simplifying -45 + w = 0 Solving -45 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '45' to each side of the equation. -45 + 45 + w = 0 + 45 Combine like terms: -45 + 45 = 0 0 + w = 0 + 45 w = 0 + 45 Combine like terms: 0 + 45 = 45 w = 45 Simplifying w = 45Subproblem 2
Set the factor '(5 + -1w)' equal to zero and attempt to solve: Simplifying 5 + -1w = 0 Solving 5 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1w = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1w = 0 + -5 -1w = 0 + -5 Combine like terms: 0 + -5 = -5 -1w = -5 Divide each side by '-1'. w = 5 Simplifying w = 5Solution
w = {45, 5}
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