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Simplifying 40b2 + 67bw + 28w2 = 0 Reorder the terms: 67bw + 40b2 + 28w2 = 0 Solving 67bw + 40b2 + 28w2 = 0 Solving for variable 'b'. Factor a trinomial. (5b + 4w)(8b + 7w) = 0Subproblem 1
Set the factor '(5b + 4w)' equal to zero and attempt to solve: Simplifying 5b + 4w = 0 Solving 5b + 4w = 0 Move all terms containing b to the left, all other terms to the right. Add '-4w' to each side of the equation. 5b + 4w + -4w = 0 + -4w Combine like terms: 4w + -4w = 0 5b + 0 = 0 + -4w 5b = 0 + -4w Remove the zero: 5b = -4w Divide each side by '5'. b = -0.8w Simplifying b = -0.8wSubproblem 2
Set the factor '(8b + 7w)' equal to zero and attempt to solve: Simplifying 8b + 7w = 0 Solving 8b + 7w = 0 Move all terms containing b to the left, all other terms to the right. Add '-7w' to each side of the equation. 8b + 7w + -7w = 0 + -7w Combine like terms: 7w + -7w = 0 8b + 0 = 0 + -7w 8b = 0 + -7w Remove the zero: 8b = -7w Divide each side by '8'. b = -0.875w Simplifying b = -0.875wSolution
b = {-0.8w, -0.875w}
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