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Simplifying 40r2 + 67rw + 28w2 = 0 Reorder the terms: 67rw + 40r2 + 28w2 = 0 Solving 67rw + 40r2 + 28w2 = 0 Solving for variable 'r'. Factor a trinomial. (5r + 4w)(8r + 7w) = 0Subproblem 1
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 = -0.8wSubproblem 2
Set the factor '(8r + 7w)' equal to zero and attempt to solve: Simplifying 8r + 7w = 0 Solving 8r + 7w = 0 Move all terms containing r to the left, all other terms to the right. Add '-7w' to each side of the equation. 8r + 7w + -7w = 0 + -7w Combine like terms: 7w + -7w = 0 8r + 0 = 0 + -7w 8r = 0 + -7w Remove the zero: 8r = -7w Divide each side by '8'. r = -0.875w Simplifying r = -0.875wSolution
r = {-0.8w, -0.875w}
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