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Simplifying 0 = 21x2 + 41x + 10 Reorder the terms: 0 = 10 + 41x + 21x2 Solving 0 = 10 + 41x + 21x2 Solving for variable 'x'. Combine like terms: 0 + -10 = -10 -10 + -41x + -21x2 = 10 + 41x + 21x2 + -10 + -41x + -21x2 Reorder the terms: -10 + -41x + -21x2 = 10 + -10 + 41x + -41x + 21x2 + -21x2 Combine like terms: 10 + -10 = 0 -10 + -41x + -21x2 = 0 + 41x + -41x + 21x2 + -21x2 -10 + -41x + -21x2 = 41x + -41x + 21x2 + -21x2 Combine like terms: 41x + -41x = 0 -10 + -41x + -21x2 = 0 + 21x2 + -21x2 -10 + -41x + -21x2 = 21x2 + -21x2 Combine like terms: 21x2 + -21x2 = 0 -10 + -41x + -21x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(10 + 41x + 21x2) = 0 Factor a trinomial. -1((5 + 3x)(2 + 7x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(5 + 3x)' equal to zero and attempt to solve: Simplifying 5 + 3x = 0 Solving 5 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 3x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3x = 0 + -5 3x = 0 + -5 Combine like terms: 0 + -5 = -5 3x = -5 Divide each side by '3'. x = -1.666666667 Simplifying x = -1.666666667Subproblem 2
Set the factor '(2 + 7x)' equal to zero and attempt to solve: Simplifying 2 + 7x = 0 Solving 2 + 7x = 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 + 7x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 7x = 0 + -2 7x = 0 + -2 Combine like terms: 0 + -2 = -2 7x = -2 Divide each side by '7'. x = -0.2857142857 Simplifying x = -0.2857142857Solution
x = {-1.666666667, -0.2857142857}
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