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Simplifying 40r2 + 57rw + 20w2 = 0 Reorder the terms: 57rw + 40r2 + 20w2 = 0 Solving 57rw + 40r2 + 20w2 = 0 Solving for variable 'r'. Factor a trinomial. (8r + 5w)(5r + 4w) = 0Subproblem 1
Set the factor '(8r + 5w)' equal to zero and attempt to solve: Simplifying 8r + 5w = 0 Solving 8r + 5w = 0 Move all terms containing r to the left, all other terms to the right. Add '-5w' to each side of the equation. 8r + 5w + -5w = 0 + -5w Combine like terms: 5w + -5w = 0 8r + 0 = 0 + -5w 8r = 0 + -5w Remove the zero: 8r = -5w Divide each side by '8'. r = -0.625w Simplifying r = -0.625wSubproblem 2
Set the factor '(5r + 4w)' equal to zero and attempt to solve: Simplifying 5r + 4w = 0 Solving 5r + 4w = 0 Move all terms containing r to the left, all other terms to the right. Add '-4w' to each side of the equation. 5r + 4w + -4w = 0 + -4w Combine like terms: 4w + -4w = 0 5r + 0 = 0 + -4w 5r = 0 + -4w Remove the zero: 5r = -4w Divide each side by '5'. r = -0.8w Simplifying r = -0.8wSolution
r = {-0.625w, -0.8w}
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