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Simplifying -2x2 + -4xb + 30b2 = 0 Reorder the terms: -4bx + 30b2 + -2x2 = 0 Solving -4bx + 30b2 + -2x2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '2'. 2(-2bx + 15b2 + -1x2) = 0 Factor a trinomial. 2((3b + -1x)(5b + x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3b + -1x)' equal to zero and attempt to solve: Simplifying 3b + -1x = 0 Solving 3b + -1x = 0 Move all terms containing b to the left, all other terms to the right. Add 'x' to each side of the equation. 3b + -1x + x = 0 + x Combine like terms: -1x + x = 0 3b + 0 = 0 + x 3b = 0 + x Remove the zero: 3b = x Divide each side by '3'. b = 0.3333333333x Simplifying b = 0.3333333333xSubproblem 2
Set the factor '(5b + x)' equal to zero and attempt to solve: Simplifying 5b + x = 0 Solving 5b + x = 0 Move all terms containing b to the left, all other terms to the right. Add '-1x' to each side of the equation. 5b + x + -1x = 0 + -1x Combine like terms: x + -1x = 0 5b + 0 = 0 + -1x 5b = 0 + -1x Remove the zero: 5b = -1x Divide each side by '5'. b = -0.2x Simplifying b = -0.2xSolution
b = {0.3333333333x, -0.2x}
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