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Simplifying (9x + 1)(10x + 2) = 0 Reorder the terms: (1 + 9x)(10x + 2) = 0 Reorder the terms: (1 + 9x)(2 + 10x) = 0 Multiply (1 + 9x) * (2 + 10x) (1(2 + 10x) + 9x * (2 + 10x)) = 0 ((2 * 1 + 10x * 1) + 9x * (2 + 10x)) = 0 ((2 + 10x) + 9x * (2 + 10x)) = 0 (2 + 10x + (2 * 9x + 10x * 9x)) = 0 (2 + 10x + (18x + 90x2)) = 0 Combine like terms: 10x + 18x = 28x (2 + 28x + 90x2) = 0 Solving 2 + 28x + 90x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(1 + 14x + 45x2) = 0 Factor a trinomial. 2((1 + 5x)(1 + 9x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + 5x)' equal to zero and attempt to solve: Simplifying 1 + 5x = 0 Solving 1 + 5x = 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 + 5x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 5x = 0 + -1 5x = 0 + -1 Combine like terms: 0 + -1 = -1 5x = -1 Divide each side by '5'. x = -0.2 Simplifying x = -0.2Subproblem 2
Set the factor '(1 + 9x)' equal to zero and attempt to solve: Simplifying 1 + 9x = 0 Solving 1 + 9x = 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 + 9x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 9x = 0 + -1 9x = 0 + -1 Combine like terms: 0 + -1 = -1 9x = -1 Divide each side by '9'. x = -0.1111111111 Simplifying x = -0.1111111111Solution
x = {-0.2, -0.1111111111}
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