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Simplifying x2 + bx = 6b2 Reorder the terms: bx + x2 = 6b2 Solving bx + x2 = 6b2 Solving for variable 'b'. Reorder the terms: bx + -6b2 + x2 = 6b2 + -6b2 Combine like terms: 6b2 + -6b2 = 0 bx + -6b2 + x2 = 0 Factor a trinomial. (-3b + -1x)(2b + -1x) = 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 + -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 = {-0.3333333333x, 0.5x}
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