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Simplifying 102x2 + 201x + 75 = 0 Reorder the terms: 75 + 201x + 102x2 = 0 Solving 75 + 201x + 102x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(25 + 67x + 34x2) = 0 Factor a trinomial. 3((25 + 17x)(1 + 2x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(25 + 17x)' equal to zero and attempt to solve: Simplifying 25 + 17x = 0 Solving 25 + 17x = 0 Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + 17x = 0 + -25 Combine like terms: 25 + -25 = 0 0 + 17x = 0 + -25 17x = 0 + -25 Combine like terms: 0 + -25 = -25 17x = -25 Divide each side by '17'. x = -1.470588235 Simplifying x = -1.470588235Subproblem 2
Set the factor '(1 + 2x)' equal to zero and attempt to solve: Simplifying 1 + 2x = 0 Solving 1 + 2x = 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 + 2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2x = 0 + -1 2x = 0 + -1 Combine like terms: 0 + -1 = -1 2x = -1 Divide each side by '2'. x = -0.5 Simplifying x = -0.5Solution
x = {-1.470588235, -0.5}
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