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Simplifying 10x2 = 3x + 1 Reorder the terms: 10x2 = 1 + 3x Solving 10x2 = 1 + 3x Solving for variable 'x'. Reorder the terms: -1 + -3x + 10x2 = 1 + 3x + -1 + -3x Reorder the terms: -1 + -3x + 10x2 = 1 + -1 + 3x + -3x Combine like terms: 1 + -1 = 0 -1 + -3x + 10x2 = 0 + 3x + -3x -1 + -3x + 10x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -1 + -3x + 10x2 = 0 Factor a trinomial. (-1 + -5x)(1 + -2x) = 0Subproblem 1
Set the factor '(-1 + -5x)' equal to zero and attempt to solve: Simplifying -1 + -5x = 0 Solving -1 + -5x = 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 + -5x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -5x = 0 + 1 -5x = 0 + 1 Combine like terms: 0 + 1 = 1 -5x = 1 Divide each side by '-5'. x = -0.2 Simplifying x = -0.2Subproblem 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 = {-0.2, 0.5}
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