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Simplifying x(9x + 2) + -7 = 0 Reorder the terms: x(2 + 9x) + -7 = 0 (2 * x + 9x * x) + -7 = 0 (2x + 9x^{2}) + -7 = 0 Reorder the terms: -7 + 2x + 9x^{2}= 0 Solving -7 + 2x + 9x^{2}= 0 Solving for variable 'x'. Factor a trinomial. (-1 + -1x)(7 + -9x) = 0## Subproblem 1

Set the factor '(-1 + -1x)' equal to zero and attempt to solve: Simplifying -1 + -1x = 0 Solving -1 + -1x = 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 + -1x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1x = 0 + 1 -1x = 0 + 1 Combine like terms: 0 + 1 = 1 -1x = 1 Divide each side by '-1'. x = -1 Simplifying x = -1## Subproblem 2

Set the factor '(7 + -9x)' equal to zero and attempt to solve: Simplifying 7 + -9x = 0 Solving 7 + -9x = 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 + -9x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -9x = 0 + -7 -9x = 0 + -7 Combine like terms: 0 + -7 = -7 -9x = -7 Divide each side by '-9'. x = 0.7777777778 Simplifying x = 0.7777777778## Solution

x = {-1, 0.7777777778}

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