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Simplifying 0 = (11x + 11)(11x + 10) Reorder the terms: 0 = (11 + 11x)(11x + 10) Reorder the terms: 0 = (11 + 11x)(10 + 11x) Multiply (11 + 11x) * (10 + 11x) 0 = (11(10 + 11x) + 11x * (10 + 11x)) 0 = ((10 * 11 + 11x * 11) + 11x * (10 + 11x)) 0 = ((110 + 121x) + 11x * (10 + 11x)) 0 = (110 + 121x + (10 * 11x + 11x * 11x)) 0 = (110 + 121x + (110x + 121x2)) Combine like terms: 121x + 110x = 231x 0 = (110 + 231x + 121x2) Solving 0 = 110 + 231x + 121x2 Solving for variable 'x'. Combine like terms: 0 + -110 = -110 -110 + -231x + -121x2 = 110 + 231x + 121x2 + -110 + -231x + -121x2 Reorder the terms: -110 + -231x + -121x2 = 110 + -110 + 231x + -231x + 121x2 + -121x2 Combine like terms: 110 + -110 = 0 -110 + -231x + -121x2 = 0 + 231x + -231x + 121x2 + -121x2 -110 + -231x + -121x2 = 231x + -231x + 121x2 + -121x2 Combine like terms: 231x + -231x = 0 -110 + -231x + -121x2 = 0 + 121x2 + -121x2 -110 + -231x + -121x2 = 121x2 + -121x2 Combine like terms: 121x2 + -121x2 = 0 -110 + -231x + -121x2 = 0 Factor out the Greatest Common Factor (GCF), '-11'. -11(10 + 21x + 11x2) = 0 Factor a trinomial. -11((1 + x)(10 + 11x)) = 0 Ignore the factor -11.Subproblem 1
Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Subproblem 2
Set the factor '(10 + 11x)' equal to zero and attempt to solve: Simplifying 10 + 11x = 0 Solving 10 + 11x = 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 + 11x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 11x = 0 + -10 11x = 0 + -10 Combine like terms: 0 + -10 = -10 11x = -10 Divide each side by '11'. x = -0.9090909091 Simplifying x = -0.9090909091Solution
x = {-1, -0.9090909091}
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