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Simplifying (2x + 1)(x) = 45 Reorder the terms: (1 + 2x)(x) = 45 Reorder the terms for easier multiplication: x(1 + 2x) = 45 (1 * x + 2x * x) = 45 (1x + 2x2) = 45 Solving 1x + 2x2 = 45 Solving for variable 'x'. Reorder the terms: -45 + 1x + 2x2 = 45 + -45 Combine like terms: 45 + -45 = 0 -45 + 1x + 2x2 = 0 Factor a trinomial. (-5 + -1x)(9 + -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 '(9 + -2x)' equal to zero and attempt to solve: Simplifying 9 + -2x = 0 Solving 9 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -2x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -2x = 0 + -9 -2x = 0 + -9 Combine like terms: 0 + -9 = -9 -2x = -9 Divide each side by '-2'. x = 4.5 Simplifying x = 4.5Solution
x = {-5, 4.5}
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