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Simplifying (5x2 + -2x + 3) + -1(3x2 + -3x + 4) = 0 Reorder the terms: (3 + -2x + 5x2) + -1(3x2 + -3x + 4) = 0 Remove parenthesis around (3 + -2x + 5x2) 3 + -2x + 5x2 + -1(3x2 + -3x + 4) = 0 Reorder the terms: 3 + -2x + 5x2 + -1(4 + -3x + 3x2) = 0 3 + -2x + 5x2 + (4 * -1 + -3x * -1 + 3x2 * -1) = 0 3 + -2x + 5x2 + (-4 + 3x + -3x2) = 0 Reorder the terms: 3 + -4 + -2x + 3x + 5x2 + -3x2 = 0 Combine like terms: 3 + -4 = -1 -1 + -2x + 3x + 5x2 + -3x2 = 0 Combine like terms: -2x + 3x = 1x -1 + 1x + 5x2 + -3x2 = 0 Combine like terms: 5x2 + -3x2 = 2x2 -1 + 1x + 2x2 = 0 Solving -1 + 1x + 2x2 = 0 Solving for variable 'x'. Factor a trinomial. (-1 + -1x)(1 + -2x) = 0Subproblem 1
Set the factor '(-1 + -1x)' equal to zero and attempt to solve: Simplifying -1 + -1x = 0 Solving -1 + -1x = 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 + -1x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1x = 0 + 1 -1x = 0 + 1 Combine like terms: 0 + 1 = 1 -1x = 1 Divide each side by '-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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