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Simplifying a * x2 + -1(a + -1b) * x = 0 Multiply a * x2 ax2 + -1(a + -1b) * x = 0 Reorder the terms for easier multiplication: ax2 + -1x(a + -1b) = 0 ax2 + (a * -1x + -1b * -1x) = 0 ax2 + (-1ax + 1bx) = 0 Reorder the terms: -1ax + ax2 + 1bx = 0 Solving -1ax + ax2 + 1bx = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1bx' to each side of the equation. -1ax + ax2 + 1bx + -1bx = 0 + -1bx Combine like terms: 1bx + -1bx = 0 -1ax + ax2 + 0 = 0 + -1bx -1ax + ax2 = 0 + -1bx Remove the zero: -1ax + ax2 = -1bx Combine like terms: -1bx + bx = 0 -1ax + ax2 + bx = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-1a + ax + b) = 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 '(-1a + ax + b)' equal to zero and attempt to solve: Simplifying -1a + ax + b = 0 Solving -1a + ax + b = 0 Move all terms containing a to the left, all other terms to the right. Add '-1b' to each side of the equation. -1a + ax + b + -1b = 0 + -1b Combine like terms: b + -1b = 0 -1a + ax + 0 = 0 + -1b -1a + ax = 0 + -1b Remove the zero: -1a + ax = -1b 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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