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Simplifying 6(x + 1) + 2 = 3x(2 + x) Reorder the terms: 6(1 + x) + 2 = 3x(2 + x) (1 * 6 + x * 6) + 2 = 3x(2 + x) (6 + 6x) + 2 = 3x(2 + x) Reorder the terms: 6 + 2 + 6x = 3x(2 + x) Combine like terms: 6 + 2 = 8 8 + 6x = 3x(2 + x) 8 + 6x = (2 * 3x + x * 3x) 8 + 6x = (6x + 3x2) Add '-6x' to each side of the equation. 8 + 6x + -6x = 6x + -6x + 3x2 Combine like terms: 6x + -6x = 0 8 + 0 = 6x + -6x + 3x2 8 = 6x + -6x + 3x2 Combine like terms: 6x + -6x = 0 8 = 0 + 3x2 8 = 3x2 Solving 8 = 3x2 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3x2' to each side of the equation. 8 + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 8 + -3x2 = 0 Add '-8' to each side of the equation. 8 + -8 + -3x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -3x2 = 0 + -8 -3x2 = 0 + -8 Combine like terms: 0 + -8 = -8 -3x2 = -8 Divide each side by '-3'. x2 = 2.666666667 Simplifying x2 = 2.666666667 Take the square root of each side: x = {-1.632993162, 1.632993162}
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