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Simplifying 56w2 + 23wr + -63r2 = 0 Reorder the terms: 23rw + -63r2 + 56w2 = 0 Solving 23rw + -63r2 + 56w2 = 0 Solving for variable 'r'. Factor a trinomial. (-9r + -7w)(7r + -8w) = 0Subproblem 1
Set the factor '(-9r + -7w)' equal to zero and attempt to solve: Simplifying -9r + -7w = 0 Solving -9r + -7w = 0 Move all terms containing r to the left, all other terms to the right. Add '7w' to each side of the equation. -9r + -7w + 7w = 0 + 7w Combine like terms: -7w + 7w = 0 -9r + 0 = 0 + 7w -9r = 0 + 7w Remove the zero: -9r = 7w Divide each side by '-9'. r = -0.7777777778w Simplifying r = -0.7777777778wSubproblem 2
Set the factor '(7r + -8w)' equal to zero and attempt to solve: Simplifying 7r + -8w = 0 Solving 7r + -8w = 0 Move all terms containing r to the left, all other terms to the right. Add '8w' to each side of the equation. 7r + -8w + 8w = 0 + 8w Combine like terms: -8w + 8w = 0 7r + 0 = 0 + 8w 7r = 0 + 8w Remove the zero: 7r = 8w Divide each side by '7'. r = 1.142857143w Simplifying r = 1.142857143wSolution
r = {-0.7777777778w, 1.142857143w}
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