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Simplifying (3x2 + -4x + -2x3 + 3) + -1(5x2 + -7x + -2x3 + 4) = 0 Reorder the terms: (3 + -4x + 3x2 + -2x3) + -1(5x2 + -7x + -2x3 + 4) = 0 Remove parenthesis around (3 + -4x + 3x2 + -2x3) 3 + -4x + 3x2 + -2x3 + -1(5x2 + -7x + -2x3 + 4) = 0 Reorder the terms: 3 + -4x + 3x2 + -2x3 + -1(4 + -7x + 5x2 + -2x3) = 0 3 + -4x + 3x2 + -2x3 + (4 * -1 + -7x * -1 + 5x2 * -1 + -2x3 * -1) = 0 3 + -4x + 3x2 + -2x3 + (-4 + 7x + -5x2 + 2x3) = 0 Reorder the terms: 3 + -4 + -4x + 7x + 3x2 + -5x2 + -2x3 + 2x3 = 0 Combine like terms: 3 + -4 = -1 -1 + -4x + 7x + 3x2 + -5x2 + -2x3 + 2x3 = 0 Combine like terms: -4x + 7x = 3x -1 + 3x + 3x2 + -5x2 + -2x3 + 2x3 = 0 Combine like terms: 3x2 + -5x2 = -2x2 -1 + 3x + -2x2 + -2x3 + 2x3 = 0 Combine like terms: -2x3 + 2x3 = 0 -1 + 3x + -2x2 + 0 = 0 -1 + 3x + -2x2 = 0 Solving -1 + 3x + -2x2 = 0 Solving for variable 'x'. Factor a trinomial. (-1 + x)(1 + -2x) = 0Subproblem 1
Set the factor '(-1 + x)' equal to zero and attempt to solve: Simplifying -1 + x = 0 Solving -1 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0 + 1 x = 0 + 1 Combine like terms: 0 + 1 = 1 x = 1 Simplifying x = 1Subproblem 2
Set the factor '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5Solution
x = {1, 0.5}
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