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Simplifying 0 = 21x2 + 78x + -24 Reorder the terms: 0 = -24 + 78x + 21x2 Solving 0 = -24 + 78x + 21x2 Solving for variable 'x'. Combine like terms: 0 + 24 = 24 24 + -78x + -21x2 = -24 + 78x + 21x2 + 24 + -78x + -21x2 Reorder the terms: 24 + -78x + -21x2 = -24 + 24 + 78x + -78x + 21x2 + -21x2 Combine like terms: -24 + 24 = 0 24 + -78x + -21x2 = 0 + 78x + -78x + 21x2 + -21x2 24 + -78x + -21x2 = 78x + -78x + 21x2 + -21x2 Combine like terms: 78x + -78x = 0 24 + -78x + -21x2 = 0 + 21x2 + -21x2 24 + -78x + -21x2 = 21x2 + -21x2 Combine like terms: 21x2 + -21x2 = 0 24 + -78x + -21x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(8 + -26x + -7x2) = 0 Factor a trinomial. 3((2 + -7x)(4 + x)) = 0 Ignore the factor 3.Subproblem 1
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 = 0.2857142857Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Solution
x = {0.2857142857, -4}
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