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Simplifying 54x2 + 438x + 420 = 0 Reorder the terms: 420 + 438x + 54x2 = 0 Solving 420 + 438x + 54x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(70 + 73x + 9x2) = 0 Factor a trinomial. 6((7 + x)(10 + 9x)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(7 + x)' equal to zero and attempt to solve: Simplifying 7 + x = 0 Solving 7 + x = 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 + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x = 0 + -7 x = 0 + -7 Combine like terms: 0 + -7 = -7 x = -7 Simplifying x = -7Subproblem 2
Set the factor '(10 + 9x)' equal to zero and attempt to solve: Simplifying 10 + 9x = 0 Solving 10 + 9x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + 9x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 9x = 0 + -10 9x = 0 + -10 Combine like terms: 0 + -10 = -10 9x = -10 Divide each side by '9'. x = -1.111111111 Simplifying x = -1.111111111Solution
x = {-7, -1.111111111}
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