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Simplifying w(w + -32) = 8025 Reorder the terms: w(-32 + w) = 8025 (-32 * w + w * w) = 8025 (-32w + w2) = 8025 Solving -32w + w2 = 8025 Solving for variable 'w'. Reorder the terms: -8025 + -32w + w2 = 8025 + -8025 Combine like terms: 8025 + -8025 = 0 -8025 + -32w + w2 = 0 Factor a trinomial. (-75 + -1w)(107 + -1w) = 0Subproblem 1
Set the factor '(-75 + -1w)' equal to zero and attempt to solve: Simplifying -75 + -1w = 0 Solving -75 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '75' to each side of the equation. -75 + 75 + -1w = 0 + 75 Combine like terms: -75 + 75 = 0 0 + -1w = 0 + 75 -1w = 0 + 75 Combine like terms: 0 + 75 = 75 -1w = 75 Divide each side by '-1'. w = -75 Simplifying w = -75Subproblem 2
Set the factor '(107 + -1w)' equal to zero and attempt to solve: Simplifying 107 + -1w = 0 Solving 107 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-107' to each side of the equation. 107 + -107 + -1w = 0 + -107 Combine like terms: 107 + -107 = 0 0 + -1w = 0 + -107 -1w = 0 + -107 Combine like terms: 0 + -107 = -107 -1w = -107 Divide each side by '-1'. w = 107 Simplifying w = 107Solution
w = {-75, 107}
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