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Simplifying 0 = x2 + -1bx + -6b2 Reorder the terms: 0 = -1bx + -6b2 + x2 Solving 0 = -1bx + -6b2 + x2 Solving for variable 'b'. Remove the zero: bx + 6b2 + -1x2 = -1bx + -6b2 + x2 + bx + 6b2 + -1x2 Reorder the terms: bx + 6b2 + -1x2 = -1bx + bx + -6b2 + 6b2 + x2 + -1x2 Combine like terms: -1bx + bx = 0 bx + 6b2 + -1x2 = 0 + -6b2 + 6b2 + x2 + -1x2 bx + 6b2 + -1x2 = -6b2 + 6b2 + x2 + -1x2 Combine like terms: -6b2 + 6b2 = 0 bx + 6b2 + -1x2 = 0 + x2 + -1x2 bx + 6b2 + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 bx + 6b2 + -1x2 = 0 Factor a trinomial. (3b + -1x)(2b + x) = 0Subproblem 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 '(2b + x)' equal to zero and attempt to solve: Simplifying 2b + x = 0 Solving 2b + x = 0 Move all terms containing b to the left, all other terms to the right. Add '-1x' to each side of the equation. 2b + x + -1x = 0 + -1x Combine like terms: x + -1x = 0 2b + 0 = 0 + -1x 2b = 0 + -1x Remove the zero: 2b = -1x Divide each side by '2'. b = -0.5x Simplifying b = -0.5xSolution
b = {0.3333333333x, -0.5x}
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