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Simplifying 400x2 + -200x + 25 = 1 Reorder the terms: 25 + -200x + 400x2 = 1 Solving 25 + -200x + 400x2 = 1 Solving for variable 'x'. Reorder the terms: 25 + -1 + -200x + 400x2 = 1 + -1 Combine like terms: 25 + -1 = 24 24 + -200x + 400x2 = 1 + -1 Combine like terms: 1 + -1 = 0 24 + -200x + 400x2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(3 + -25x + 50x2) = 0 Factor a trinomial. 8((1 + -5x)(3 + -10x)) = 0 Ignore the factor 8.Subproblem 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 '(3 + -10x)' equal to zero and attempt to solve: Simplifying 3 + -10x = 0 Solving 3 + -10x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -10x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -10x = 0 + -3 -10x = 0 + -3 Combine like terms: 0 + -3 = -3 -10x = -3 Divide each side by '-10'. x = 0.3 Simplifying x = 0.3Solution
x = {0.2, 0.3}
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