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Simplifying (x3 + 1)(x + 1) + 2ax2 = 0 Reorder the terms: (1 + x3)(x + 1) + 2ax2 = 0 Reorder the terms: (1 + x3)(1 + x) + 2ax2 = 0 Multiply (1 + x3) * (1 + x) (1(1 + x) + x3(1 + x)) + 2ax2 = 0 ((1 * 1 + x * 1) + x3(1 + x)) + 2ax2 = 0 ((1 + 1x) + x3(1 + x)) + 2ax2 = 0 (1 + 1x + (1 * x3 + x * x3)) + 2ax2 = 0 (1 + 1x + (1x3 + x4)) + 2ax2 = 0 (1 + 1x + 1x3 + x4) + 2ax2 = 0 Reorder the terms: 1 + 2ax2 + 1x + 1x3 + x4 = 0 Solving 1 + 2ax2 + 1x + 1x3 + x4 = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + 2ax2 + 1x + 1x3 + -1 + x4 = 0 + -1 Reorder the terms: 1 + -1 + 2ax2 + 1x + 1x3 + x4 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2ax2 + 1x + 1x3 + x4 = 0 + -1 2ax2 + 1x + 1x3 + x4 = 0 + -1 Combine like terms: 0 + -1 = -1 2ax2 + 1x + 1x3 + x4 = -1 Add '-1x' to each side of the equation. 2ax2 + 1x + 1x3 + -1x + x4 = -1 + -1x Reorder the terms: 2ax2 + 1x + -1x + 1x3 + x4 = -1 + -1x Combine like terms: 1x + -1x = 0 2ax2 + 0 + 1x3 + x4 = -1 + -1x 2ax2 + 1x3 + x4 = -1 + -1x Add '-1x3' to each side of the equation. 2ax2 + 1x3 + -1x3 + x4 = -1 + -1x + -1x3 Combine like terms: 1x3 + -1x3 = 0 2ax2 + 0 + x4 = -1 + -1x + -1x3 2ax2 + x4 = -1 + -1x + -1x3 Add '-1x4' to each side of the equation. 2ax2 + x4 + -1x4 = -1 + -1x + -1x3 + -1x4 Combine like terms: x4 + -1x4 = 0 2ax2 + 0 = -1 + -1x + -1x3 + -1x4 2ax2 = -1 + -1x + -1x3 + -1x4 Divide each side by '2x2'. a = -0.5x-2 + -0.5x-1 + -0.5x + -0.5x2 Simplifying a = -0.5x-2 + -0.5x-1 + -0.5x + -0.5x2
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