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Simplifying ax(x + 1) = bx2 Reorder the terms: ax(1 + x) = bx2 (1 * ax + x * ax) = bx2 (1ax + ax2) = bx2 Solving 1ax + ax2 = bx2 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Combine like terms: bx2 + -1bx2 = 0 1ax + ax2 + -1bx2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(a + ax + -1bx) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing a to the left, all other terms to the right. Add '-1x' to each side of the equation. x + -1x = 0 + -1x Remove the zero: 0 = -1x Simplifying 0 = -1x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(a + ax + -1bx)' equal to zero and attempt to solve: Simplifying a + ax + -1bx = 0 Solving a + ax + -1bx = 0 Move all terms containing a to the left, all other terms to the right. Add 'bx' to each side of the equation. a + ax + -1bx + bx = 0 + bx Combine like terms: -1bx + bx = 0 a + ax + 0 = 0 + bx a + ax = 0 + bx Remove the zero: a + ax = bx The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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