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Simplifying 8x2 + -10bx + -3b2 = 0 Reorder the terms: -10bx + -3b2 + 8x2 = 0 Solving -10bx + -3b2 + 8x2 = 0 Solving for variable 'b'. Factor a trinomial. (-1b + -4x)(3b + -2x) = 0Subproblem 1
Set the factor '(-1b + -4x)' equal to zero and attempt to solve: Simplifying -1b + -4x = 0 Solving -1b + -4x = 0 Move all terms containing b to the left, all other terms to the right. Add '4x' to each side of the equation. -1b + -4x + 4x = 0 + 4x Combine like terms: -4x + 4x = 0 -1b + 0 = 0 + 4x -1b = 0 + 4x Remove the zero: -1b = 4x Divide each side by '-1'. b = -4x Simplifying b = -4xSubproblem 2
Set the factor '(3b + -2x)' equal to zero and attempt to solve: Simplifying 3b + -2x = 0 Solving 3b + -2x = 0 Move all terms containing b to the left, all other terms to the right. Add '2x' to each side of the equation. 3b + -2x + 2x = 0 + 2x Combine like terms: -2x + 2x = 0 3b + 0 = 0 + 2x 3b = 0 + 2x Remove the zero: 3b = 2x Divide each side by '3'. b = 0.6666666667x Simplifying b = 0.6666666667xSolution
b = {-4x, 0.6666666667x}
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