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Simplifying 4x + 9 = x(2x + 1) Reorder the terms: 9 + 4x = x(2x + 1) Reorder the terms: 9 + 4x = x(1 + 2x) 9 + 4x = (1 * x + 2x * x) 9 + 4x = (1x + 2x2) Solving 9 + 4x = 1x + 2x2 Solving for variable 'x'. Combine like terms: 4x + -1x = 3x 9 + 3x + -2x2 = 1x + 2x2 + -1x + -2x2 Reorder the terms: 9 + 3x + -2x2 = 1x + -1x + 2x2 + -2x2 Combine like terms: 1x + -1x = 0 9 + 3x + -2x2 = 0 + 2x2 + -2x2 9 + 3x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 9 + 3x + -2x2 = 0 Factor a trinomial. (3 + -1x)(3 + 2x) = 0Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Subproblem 2
Set the factor '(3 + 2x)' equal to zero and attempt to solve: Simplifying 3 + 2x = 0 Solving 3 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x = 0 + -3 2x = 0 + -3 Combine like terms: 0 + -3 = -3 2x = -3 Divide each side by '2'. x = -1.5 Simplifying x = -1.5Solution
x = {3, -1.5}
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