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Simplifying 40r4 + 50r3b + -35r2b2 = 0 Reorder the terms: 50br3 + -35b2r2 + 40r4 = 0 Solving 50br3 + -35b2r2 + 40r4 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '5r2'. 5r2(10br + -7b2 + 8r2) = 0 Factor a trinomial. 5r2((-7b + -4r)(b + -2r)) = 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 '(-7b + -4r)' equal to zero and attempt to solve: Simplifying -7b + -4r = 0 Solving -7b + -4r = 0 Move all terms containing b to the left, all other terms to the right. Add '4r' to each side of the equation. -7b + -4r + 4r = 0 + 4r Combine like terms: -4r + 4r = 0 -7b + 0 = 0 + 4r -7b = 0 + 4r Remove the zero: -7b = 4r Divide each side by '-7'. b = -0.5714285714r Simplifying b = -0.5714285714rSubproblem 3
Set the factor '(b + -2r)' equal to zero and attempt to solve: Simplifying b + -2r = 0 Solving b + -2r = 0 Move all terms containing b to the left, all other terms to the right. Add '2r' to each side of the equation. b + -2r + 2r = 0 + 2r Combine like terms: -2r + 2r = 0 b + 0 = 0 + 2r b = 0 + 2r Remove the zero: b = 2r Simplifying b = 2rSolution
b = {-0.5714285714r, 2r}
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