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Simplifying (3x + 1)(3x + 1) = 7x2 + -3x + 6 Reorder the terms: (1 + 3x)(3x + 1) = 7x2 + -3x + 6 Reorder the terms: (1 + 3x)(1 + 3x) = 7x2 + -3x + 6 Multiply (1 + 3x) * (1 + 3x) (1(1 + 3x) + 3x * (1 + 3x)) = 7x2 + -3x + 6 ((1 * 1 + 3x * 1) + 3x * (1 + 3x)) = 7x2 + -3x + 6 ((1 + 3x) + 3x * (1 + 3x)) = 7x2 + -3x + 6 (1 + 3x + (1 * 3x + 3x * 3x)) = 7x2 + -3x + 6 (1 + 3x + (3x + 9x2)) = 7x2 + -3x + 6 Combine like terms: 3x + 3x = 6x (1 + 6x + 9x2) = 7x2 + -3x + 6 Reorder the terms: 1 + 6x + 9x2 = 6 + -3x + 7x2 Solving 1 + 6x + 9x2 = 6 + -3x + 7x2 Solving for variable 'x'. Reorder the terms: 1 + -6 + 6x + 3x + 9x2 + -7x2 = 6 + -3x + 7x2 + -6 + 3x + -7x2 Combine like terms: 1 + -6 = -5 -5 + 6x + 3x + 9x2 + -7x2 = 6 + -3x + 7x2 + -6 + 3x + -7x2 Combine like terms: 6x + 3x = 9x -5 + 9x + 9x2 + -7x2 = 6 + -3x + 7x2 + -6 + 3x + -7x2 Combine like terms: 9x2 + -7x2 = 2x2 -5 + 9x + 2x2 = 6 + -3x + 7x2 + -6 + 3x + -7x2 Reorder the terms: -5 + 9x + 2x2 = 6 + -6 + -3x + 3x + 7x2 + -7x2 Combine like terms: 6 + -6 = 0 -5 + 9x + 2x2 = 0 + -3x + 3x + 7x2 + -7x2 -5 + 9x + 2x2 = -3x + 3x + 7x2 + -7x2 Combine like terms: -3x + 3x = 0 -5 + 9x + 2x2 = 0 + 7x2 + -7x2 -5 + 9x + 2x2 = 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 -5 + 9x + 2x2 = 0 Factor a trinomial. (-5 + -1x)(1 + -2x) = 0Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve: Simplifying -5 + -1x = 0 Solving -5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1x = 0 + 5 -1x = 0 + 5 Combine like terms: 0 + 5 = 5 -1x = 5 Divide each side by '-1'. x = -5 Simplifying x = -5Subproblem 2
Set the factor '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 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 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5Solution
x = {-5, 0.5}
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