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Simplifying -100x2 + 55x + 3 = 50x2 + -55x + 23 Reorder the terms: 3 + 55x + -100x2 = 50x2 + -55x + 23 Reorder the terms: 3 + 55x + -100x2 = 23 + -55x + 50x2 Solving 3 + 55x + -100x2 = 23 + -55x + 50x2 Solving for variable 'x'. Reorder the terms: 3 + -23 + 55x + 55x + -100x2 + -50x2 = 23 + -55x + 50x2 + -23 + 55x + -50x2 Combine like terms: 3 + -23 = -20 -20 + 55x + 55x + -100x2 + -50x2 = 23 + -55x + 50x2 + -23 + 55x + -50x2 Combine like terms: 55x + 55x = 110x -20 + 110x + -100x2 + -50x2 = 23 + -55x + 50x2 + -23 + 55x + -50x2 Combine like terms: -100x2 + -50x2 = -150x2 -20 + 110x + -150x2 = 23 + -55x + 50x2 + -23 + 55x + -50x2 Reorder the terms: -20 + 110x + -150x2 = 23 + -23 + -55x + 55x + 50x2 + -50x2 Combine like terms: 23 + -23 = 0 -20 + 110x + -150x2 = 0 + -55x + 55x + 50x2 + -50x2 -20 + 110x + -150x2 = -55x + 55x + 50x2 + -50x2 Combine like terms: -55x + 55x = 0 -20 + 110x + -150x2 = 0 + 50x2 + -50x2 -20 + 110x + -150x2 = 50x2 + -50x2 Combine like terms: 50x2 + -50x2 = 0 -20 + 110x + -150x2 = 0 Factor out the Greatest Common Factor (GCF), '10'. 10(-2 + 11x + -15x2) = 0 Factor a trinomial. 10((-2 + 5x)(1 + -3x)) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(-2 + 5x)' equal to zero and attempt to solve: Simplifying -2 + 5x = 0 Solving -2 + 5x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + 5x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 5x = 0 + 2 5x = 0 + 2 Combine like terms: 0 + 2 = 2 5x = 2 Divide each side by '5'. x = 0.4 Simplifying x = 0.4Subproblem 2
Set the factor '(1 + -3x)' equal to zero and attempt to solve: Simplifying 1 + -3x = 0 Solving 1 + -3x = 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 + -3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3x = 0 + -1 -3x = 0 + -1 Combine like terms: 0 + -1 = -1 -3x = -1 Divide each side by '-3'. x = 0.3333333333 Simplifying x = 0.3333333333Solution
x = {0.4, 0.3333333333}
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