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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. (8r + -7w)(5r + -4w) = 0Subproblem 1
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 = 0.875wSubproblem 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 = {0.875w, 0.8w}
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