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Simplifying (2x + 1)(x + 1) = 28 Reorder the terms: (1 + 2x)(x + 1) = 28 Reorder the terms: (1 + 2x)(1 + x) = 28 Multiply (1 + 2x) * (1 + x) (1(1 + x) + 2x * (1 + x)) = 28 ((1 * 1 + x * 1) + 2x * (1 + x)) = 28 ((1 + 1x) + 2x * (1 + x)) = 28 (1 + 1x + (1 * 2x + x * 2x)) = 28 (1 + 1x + (2x + 2x2)) = 28 Combine like terms: 1x + 2x = 3x (1 + 3x + 2x2) = 28 Solving 1 + 3x + 2x2 = 28 Solving for variable 'x'. Reorder the terms: 1 + -28 + 3x + 2x2 = 28 + -28 Combine like terms: 1 + -28 = -27 -27 + 3x + 2x2 = 28 + -28 Combine like terms: 28 + -28 = 0 -27 + 3x + 2x2 = 0 Factor a trinomial. (-9 + -2x)(3 + -1x) = 0Subproblem 1
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 = -4.5Subproblem 2
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 = 3Solution
x = {-4.5, 3}
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