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Simplifying 2x2 + 12bx + -32b2 = 0 Reorder the terms: 12bx + -32b2 + 2x2 = 0 Solving 12bx + -32b2 + 2x2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '2'. 2(6bx + -16b2 + x2) = 0 Factor a trinomial. 2((-8b + -1x)(2b + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-8b + -1x)' equal to zero and attempt to solve: Simplifying -8b + -1x = 0 Solving -8b + -1x = 0 Move all terms containing b to the left, all other terms to the right. Add 'x' to each side of the equation. -8b + -1x + x = 0 + x Combine like terms: -1x + x = 0 -8b + 0 = 0 + x -8b = 0 + x Remove the zero: -8b = x Divide each side by '-8'. b = -0.125x Simplifying b = -0.125xSubproblem 2
Set the factor '(2b + -1x)' equal to zero and attempt to solve: Simplifying 2b + -1x = 0 Solving 2b + -1x = 0 Move all terms containing b to the left, all other terms to the right. Add 'x' to each side of the equation. 2b + -1x + x = 0 + x Combine like terms: -1x + x = 0 2b + 0 = 0 + x 2b = 0 + x Remove the zero: 2b = x Divide each side by '2'. b = 0.5x Simplifying b = 0.5xSolution
b = {-0.125x, 0.5x}
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