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Simplifying -25x = 75x2 + -100x3 Solving -25x = 75x2 + -100x3 Solving for variable 'x'. Reorder the terms: -25x + -75x2 + 100x3 = 75x2 + -75x2 + -100x3 + 100x3 Combine like terms: 75x2 + -75x2 = 0 -25x + -75x2 + 100x3 = 0 + -100x3 + 100x3 -25x + -75x2 + 100x3 = -100x3 + 100x3 Combine like terms: -100x3 + 100x3 = 0 -25x + -75x2 + 100x3 = 0 Factor out the Greatest Common Factor (GCF), '25x'. 25x(-1 + -3x + 4x2) = 0 Factor a trinomial. 25x((-1 + -4x)(1 + -1x)) = 0 Ignore the factor 25.Subproblem 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 + -4x)' equal to zero and attempt to solve: Simplifying -1 + -4x = 0 Solving -1 + -4x = 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 + -4x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -4x = 0 + 1 -4x = 0 + 1 Combine like terms: 0 + 1 = 1 -4x = 1 Divide each side by '-4'. x = -0.25 Simplifying x = -0.25Subproblem 3
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 = 1Solution
x = {0, -0.25, 1}
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