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Simplifying 8(25x2 + -10x + 1) + 3 = -10(5x + -1) Reorder the terms: 8(1 + -10x + 25x2) + 3 = -10(5x + -1) (1 * 8 + -10x * 8 + 25x2 * 8) + 3 = -10(5x + -1) (8 + -80x + 200x2) + 3 = -10(5x + -1) Reorder the terms: 8 + 3 + -80x + 200x2 = -10(5x + -1) Combine like terms: 8 + 3 = 11 11 + -80x + 200x2 = -10(5x + -1) Reorder the terms: 11 + -80x + 200x2 = -10(-1 + 5x) 11 + -80x + 200x2 = (-1 * -10 + 5x * -10) 11 + -80x + 200x2 = (10 + -50x) Solving 11 + -80x + 200x2 = 10 + -50x Solving for variable 'x'. Reorder the terms: 11 + -10 + -80x + 50x + 200x2 = 10 + -50x + -10 + 50x Combine like terms: 11 + -10 = 1 1 + -80x + 50x + 200x2 = 10 + -50x + -10 + 50x Combine like terms: -80x + 50x = -30x 1 + -30x + 200x2 = 10 + -50x + -10 + 50x Reorder the terms: 1 + -30x + 200x2 = 10 + -10 + -50x + 50x Combine like terms: 10 + -10 = 0 1 + -30x + 200x2 = 0 + -50x + 50x 1 + -30x + 200x2 = -50x + 50x Combine like terms: -50x + 50x = 0 1 + -30x + 200x2 = 0 Factor a trinomial. (1 + -20x)(1 + -10x) = 0Subproblem 1
Set the factor '(1 + -20x)' equal to zero and attempt to solve: Simplifying 1 + -20x = 0 Solving 1 + -20x = 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 + -20x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -20x = 0 + -1 -20x = 0 + -1 Combine like terms: 0 + -1 = -1 -20x = -1 Divide each side by '-20'. x = 0.05 Simplifying x = 0.05Subproblem 2
Set the factor '(1 + -10x)' equal to zero and attempt to solve: Simplifying 1 + -10x = 0 Solving 1 + -10x = 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 + -10x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -10x = 0 + -1 -10x = 0 + -1 Combine like terms: 0 + -1 = -1 -10x = -1 Divide each side by '-10'. x = 0.1 Simplifying x = 0.1Solution
x = {0.05, 0.1}
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