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Simplifying 0 = 10x2 + -27x + 5 Reorder the terms: 0 = 5 + -27x + 10x2 Solving 0 = 5 + -27x + 10x2 Solving for variable 'x'. Combine like terms: 0 + -5 = -5 -5 + 27x + -10x2 = 5 + -27x + 10x2 + -5 + 27x + -10x2 Reorder the terms: -5 + 27x + -10x2 = 5 + -5 + -27x + 27x + 10x2 + -10x2 Combine like terms: 5 + -5 = 0 -5 + 27x + -10x2 = 0 + -27x + 27x + 10x2 + -10x2 -5 + 27x + -10x2 = -27x + 27x + 10x2 + -10x2 Combine like terms: -27x + 27x = 0 -5 + 27x + -10x2 = 0 + 10x2 + -10x2 -5 + 27x + -10x2 = 10x2 + -10x2 Combine like terms: 10x2 + -10x2 = 0 -5 + 27x + -10x2 = 0 Factor a trinomial. (-5 + 2x)(1 + -5x) = 0Subproblem 1
Set the factor '(-5 + 2x)' equal to zero and attempt to solve: Simplifying -5 + 2x = 0 Solving -5 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + 2x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 2x = 0 + 5 2x = 0 + 5 Combine like terms: 0 + 5 = 5 2x = 5 Divide each side by '2'. x = 2.5 Simplifying x = 2.5Subproblem 2
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 = 0.2Solution
x = {2.5, 0.2}
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