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Simplifying (1 + -7x)(1 + 9x) * x = 0 Reorder the terms for easier multiplication: x(1 + -7x)(1 + 9x) = 0 Multiply (1 + -7x) * (1 + 9x) x(1(1 + 9x) + -7x * (1 + 9x)) = 0 x((1 * 1 + 9x * 1) + -7x * (1 + 9x)) = 0 x((1 + 9x) + -7x * (1 + 9x)) = 0 x(1 + 9x + (1 * -7x + 9x * -7x)) = 0 x(1 + 9x + (-7x + -63x2)) = 0 Combine like terms: 9x + -7x = 2x x(1 + 2x + -63x2) = 0 (1 * x + 2x * x + -63x2 * x) = 0 (1x + 2x2 + -63x3) = 0 Solving 1x + 2x2 + -63x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(1 + 2x + -63x2) = 0 Factor a trinomial. x((1 + -7x)(1 + 9x)) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(1 + -7x)' equal to zero and attempt to solve: Simplifying 1 + -7x = 0 Solving 1 + -7x = 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 + -7x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -7x = 0 + -1 -7x = 0 + -1 Combine like terms: 0 + -1 = -1 -7x = -1 Divide each side by '-7'. x = 0.1428571429 Simplifying x = 0.1428571429Subproblem 3
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, 0.1428571429, -0.1111111111}
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