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Simplifying x2 + 4bx + -12b2 = 0 Reorder the terms: 4bx + -12b2 + x2 = 0 Solving 4bx + -12b2 + x2 = 0 Solving for variable 'b'. Factor a trinomial. (-6b + -1x)(2b + -1x) = 0Subproblem 1
Set the factor '(-6b + -1x)' equal to zero and attempt to solve: Simplifying -6b + -1x = 0 Solving -6b + -1x = 0 Move all terms containing b to the left, all other terms to the right. Add 'x' to each side of the equation. -6b + -1x + x = 0 + x Combine like terms: -1x + x = 0 -6b + 0 = 0 + x -6b = 0 + x Remove the zero: -6b = x Divide each side by '-6'. b = -0.1666666667x Simplifying b = -0.1666666667xSubproblem 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 = {-0.1666666667x, 0.5x}
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