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Simplifying 75b2 + 90bp + 27p2 = 0 Reorder the terms: 90bp + 75b2 + 27p2 = 0 Solving 90bp + 75b2 + 27p2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '3'. 3(30bp + 25b2 + 9p2) = 0 Factor a trinomial. 3((5b + 3p)(5b + 3p)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(5b + 3p)' equal to zero and attempt to solve: Simplifying 5b + 3p = 0 Solving 5b + 3p = 0 Move all terms containing b to the left, all other terms to the right. Add '-3p' to each side of the equation. 5b + 3p + -3p = 0 + -3p Combine like terms: 3p + -3p = 0 5b + 0 = 0 + -3p 5b = 0 + -3p Remove the zero: 5b = -3p Divide each side by '5'. b = -0.6p Simplifying b = -0.6pSubproblem 2
Set the factor '(5b + 3p)' equal to zero and attempt to solve: Simplifying 5b + 3p = 0 Solving 5b + 3p = 0 Move all terms containing b to the left, all other terms to the right. Add '-3p' to each side of the equation. 5b + 3p + -3p = 0 + -3p Combine like terms: 3p + -3p = 0 5b + 0 = 0 + -3p 5b = 0 + -3p Remove the zero: 5b = -3p Divide each side by '5'. b = -0.6p Simplifying b = -0.6pSolution
b = {-0.6p, -0.6p}
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