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Simplifying (x2 + 1) + (4x + 3) = 2x2 + 3x + -2 Reorder the terms: (1 + x2) + (4x + 3) = 2x2 + 3x + -2 Remove parenthesis around (1 + x2) 1 + x2 + (4x + 3) = 2x2 + 3x + -2 Reorder the terms: 1 + x2 + (3 + 4x) = 2x2 + 3x + -2 Remove parenthesis around (3 + 4x) 1 + x2 + 3 + 4x = 2x2 + 3x + -2 Reorder the terms: 1 + 3 + 4x + x2 = 2x2 + 3x + -2 Combine like terms: 1 + 3 = 4 4 + 4x + x2 = 2x2 + 3x + -2 Reorder the terms: 4 + 4x + x2 = -2 + 3x + 2x2 Solving 4 + 4x + x2 = -2 + 3x + 2x2 Solving for variable 'x'. Reorder the terms: 4 + 2 + 4x + -3x + x2 + -2x2 = -2 + 3x + 2x2 + 2 + -3x + -2x2 Combine like terms: 4 + 2 = 6 6 + 4x + -3x + x2 + -2x2 = -2 + 3x + 2x2 + 2 + -3x + -2x2 Combine like terms: 4x + -3x = 1x 6 + 1x + x2 + -2x2 = -2 + 3x + 2x2 + 2 + -3x + -2x2 Combine like terms: x2 + -2x2 = -1x2 6 + 1x + -1x2 = -2 + 3x + 2x2 + 2 + -3x + -2x2 Reorder the terms: 6 + 1x + -1x2 = -2 + 2 + 3x + -3x + 2x2 + -2x2 Combine like terms: -2 + 2 = 0 6 + 1x + -1x2 = 0 + 3x + -3x + 2x2 + -2x2 6 + 1x + -1x2 = 3x + -3x + 2x2 + -2x2 Combine like terms: 3x + -3x = 0 6 + 1x + -1x2 = 0 + 2x2 + -2x2 6 + 1x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 6 + 1x + -1x2 = 0 Factor a trinomial. (3 + -1x)(2 + x) = 0Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Solution
x = {3, -2}
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