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Simplifying 0 = 21x2 + 76x + 63 Reorder the terms: 0 = 63 + 76x + 21x2 Solving 0 = 63 + 76x + 21x2 Solving for variable 'x'. Combine like terms: 0 + -63 = -63 -63 + -76x + -21x2 = 63 + 76x + 21x2 + -63 + -76x + -21x2 Reorder the terms: -63 + -76x + -21x2 = 63 + -63 + 76x + -76x + 21x2 + -21x2 Combine like terms: 63 + -63 = 0 -63 + -76x + -21x2 = 0 + 76x + -76x + 21x2 + -21x2 -63 + -76x + -21x2 = 76x + -76x + 21x2 + -21x2 Combine like terms: 76x + -76x = 0 -63 + -76x + -21x2 = 0 + 21x2 + -21x2 -63 + -76x + -21x2 = 21x2 + -21x2 Combine like terms: 21x2 + -21x2 = 0 -63 + -76x + -21x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(63 + 76x + 21x2) = 0 Factor a trinomial. -1((7 + 3x)(9 + 7x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(7 + 3x)' equal to zero and attempt to solve: Simplifying 7 + 3x = 0 Solving 7 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 3x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 3x = 0 + -7 3x = 0 + -7 Combine like terms: 0 + -7 = -7 3x = -7 Divide each side by '3'. x = -2.333333333 Simplifying x = -2.333333333Subproblem 2
Set the factor '(9 + 7x)' equal to zero and attempt to solve: Simplifying 9 + 7x = 0 Solving 9 + 7x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 7x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 7x = 0 + -9 7x = 0 + -9 Combine like terms: 0 + -9 = -9 7x = -9 Divide each side by '7'. x = -1.285714286 Simplifying x = -1.285714286Solution
x = {-2.333333333, -1.285714286}
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