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Simplifying 0 = 25x3 + -10x2 + 1x Reorder the terms: 0 = 1x + -10x2 + 25x3 Solving 0 = 1x + -10x2 + 25x3 Solving for variable 'x'. Remove the zero: -1x + 10x2 + -25x3 = 1x + -10x2 + 25x3 + -1x + 10x2 + -25x3 Reorder the terms: -1x + 10x2 + -25x3 = 1x + -1x + -10x2 + 10x2 + 25x3 + -25x3 Combine like terms: 1x + -1x = 0 -1x + 10x2 + -25x3 = 0 + -10x2 + 10x2 + 25x3 + -25x3 -1x + 10x2 + -25x3 = -10x2 + 10x2 + 25x3 + -25x3 Combine like terms: -10x2 + 10x2 = 0 -1x + 10x2 + -25x3 = 0 + 25x3 + -25x3 -1x + 10x2 + -25x3 = 25x3 + -25x3 Combine like terms: 25x3 + -25x3 = 0 -1x + 10x2 + -25x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-1 + 10x + -25x2) = 0 Factor a trinomial. x((-1 + 5x)(1 + -5x)) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 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 = 0.2Subproblem 3
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 = {0, 0.2, 0.2}
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