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Simplifying 40r4 + 90(r3b) + -25r2b2 = 0 Reorder the terms: 90br3 + -25b2r2 + 40r4 = 0 Solving 90br3 + -25b2r2 + 40r4 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '5r2'. 5r2(18br + -5b2 + 8r2) = 0 Factor a trinomial. 5r2((-5b + -2r)(b + -4r)) = 0 Ignore the factor 5.Subproblem 1
Set the factor 'r2' equal to zero and attempt to solve: Simplifying r2 = 0 Solving r2 = 0 Move all terms containing b to the left, all other terms to the right. Add '-1r2' to each side of the equation. r2 + -1r2 = 0 + -1r2 Remove the zero: 0 = -1r2 Simplifying 0 = -1r2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-5b + -2r)' equal to zero and attempt to solve: Simplifying -5b + -2r = 0 Solving -5b + -2r = 0 Move all terms containing b to the left, all other terms to the right. Add '2r' to each side of the equation. -5b + -2r + 2r = 0 + 2r Combine like terms: -2r + 2r = 0 -5b + 0 = 0 + 2r -5b = 0 + 2r Remove the zero: -5b = 2r Divide each side by '-5'. b = -0.4r Simplifying b = -0.4rSubproblem 3
Set the factor '(b + -4r)' equal to zero and attempt to solve: Simplifying b + -4r = 0 Solving b + -4r = 0 Move all terms containing b to the left, all other terms to the right. Add '4r' to each side of the equation. b + -4r + 4r = 0 + 4r Combine like terms: -4r + 4r = 0 b + 0 = 0 + 4r b = 0 + 4r Remove the zero: b = 4r Simplifying b = 4rSolution
b = {-0.4r, 4r}
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