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Simplifying 2(a + -1) * x2 + 4(2a + 1) * x + 8a + 6 = 0 Reorder the terms: 2(-1 + a) * x2 + 4(2a + 1) * x + 8a + 6 = 0 Reorder the terms for easier multiplication: 2x2(-1 + a) + 4(2a + 1) * x + 8a + 6 = 0 (-1 * 2x2 + a * 2x2) + 4(2a + 1) * x + 8a + 6 = 0 Reorder the terms: (2ax2 + -2x2) + 4(2a + 1) * x + 8a + 6 = 0 (2ax2 + -2x2) + 4(2a + 1) * x + 8a + 6 = 0 Reorder the terms: 2ax2 + -2x2 + 4(1 + 2a) * x + 8a + 6 = 0 Reorder the terms for easier multiplication: 2ax2 + -2x2 + 4x(1 + 2a) + 8a + 6 = 0 2ax2 + -2x2 + (1 * 4x + 2a * 4x) + 8a + 6 = 0 Reorder the terms: 2ax2 + -2x2 + (8ax + 4x) + 8a + 6 = 0 2ax2 + -2x2 + (8ax + 4x) + 8a + 6 = 0 Reorder the terms: 6 + 8a + 8ax + 2ax2 + 4x + -2x2 = 0 Solving 6 + 8a + 8ax + 2ax2 + 4x + -2x2 = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + 8a + 8ax + 2ax2 + 4x + -6 + -2x2 = 0 + -6 Reorder the terms: 6 + -6 + 8a + 8ax + 2ax2 + 4x + -2x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 8a + 8ax + 2ax2 + 4x + -2x2 = 0 + -6 8a + 8ax + 2ax2 + 4x + -2x2 = 0 + -6 Combine like terms: 0 + -6 = -6 8a + 8ax + 2ax2 + 4x + -2x2 = -6 Add '-4x' to each side of the equation. 8a + 8ax + 2ax2 + 4x + -4x + -2x2 = -6 + -4x Combine like terms: 4x + -4x = 0 8a + 8ax + 2ax2 + 0 + -2x2 = -6 + -4x 8a + 8ax + 2ax2 + -2x2 = -6 + -4x Add '2x2' to each side of the equation. 8a + 8ax + 2ax2 + -2x2 + 2x2 = -6 + -4x + 2x2 Combine like terms: -2x2 + 2x2 = 0 8a + 8ax + 2ax2 + 0 = -6 + -4x + 2x2 8a + 8ax + 2ax2 = -6 + -4x + 2x2 Reorder the terms: 6 + 8a + 8ax + 2ax2 + 4x + -2x2 = -6 + -4x + 2x2 + 6 + 4x + -2x2 Reorder the terms: 6 + 8a + 8ax + 2ax2 + 4x + -2x2 = -6 + 6 + -4x + 4x + 2x2 + -2x2 Combine like terms: -6 + 6 = 0 6 + 8a + 8ax + 2ax2 + 4x + -2x2 = 0 + -4x + 4x + 2x2 + -2x2 6 + 8a + 8ax + 2ax2 + 4x + -2x2 = -4x + 4x + 2x2 + -2x2 Combine like terms: -4x + 4x = 0 6 + 8a + 8ax + 2ax2 + 4x + -2x2 = 0 + 2x2 + -2x2 6 + 8a + 8ax + 2ax2 + 4x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 6 + 8a + 8ax + 2ax2 + 4x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(3 + 4a + 4ax + ax2 + 2x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + 4a + 4ax + ax2 + 2x + -1x2)' equal to zero and attempt to solve: Simplifying 3 + 4a + 4ax + ax2 + 2x + -1x2 = 0 Solving 3 + 4a + 4ax + ax2 + 2x + -1x2 = 0 Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + 4a + 4ax + ax2 + 2x + -3 + -1x2 = 0 + -3 Reorder the terms: 3 + -3 + 4a + 4ax + ax2 + 2x + -1x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4a + 4ax + ax2 + 2x + -1x2 = 0 + -3 4a + 4ax + ax2 + 2x + -1x2 = 0 + -3 Combine like terms: 0 + -3 = -3 4a + 4ax + ax2 + 2x + -1x2 = -3 Add '-2x' to each side of the equation. 4a + 4ax + ax2 + 2x + -2x + -1x2 = -3 + -2x Combine like terms: 2x + -2x = 0 4a + 4ax + ax2 + 0 + -1x2 = -3 + -2x 4a + 4ax + ax2 + -1x2 = -3 + -2x Add 'x2' to each side of the equation. 4a + 4ax + ax2 + -1x2 + x2 = -3 + -2x + x2 Combine like terms: -1x2 + x2 = 0 4a + 4ax + ax2 + 0 = -3 + -2x + x2 4a + 4ax + ax2 = -3 + -2x + x2 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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