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Simplifying (4x + 1)(x + 1) = 52 Reorder the terms: (1 + 4x)(x + 1) = 52 Reorder the terms: (1 + 4x)(1 + x) = 52 Multiply (1 + 4x) * (1 + x) (1(1 + x) + 4x * (1 + x)) = 52 ((1 * 1 + x * 1) + 4x * (1 + x)) = 52 ((1 + 1x) + 4x * (1 + x)) = 52 (1 + 1x + (1 * 4x + x * 4x)) = 52 (1 + 1x + (4x + 4x2)) = 52 Combine like terms: 1x + 4x = 5x (1 + 5x + 4x2) = 52 Solving 1 + 5x + 4x2 = 52 Solving for variable 'x'. Reorder the terms: 1 + -52 + 5x + 4x2 = 52 + -52 Combine like terms: 1 + -52 = -51 -51 + 5x + 4x2 = 52 + -52 Combine like terms: 52 + -52 = 0 -51 + 5x + 4x2 = 0 Factor a trinomial. (-17 + -4x)(3 + -1x) = 0Subproblem 1
Set the factor '(-17 + -4x)' equal to zero and attempt to solve: Simplifying -17 + -4x = 0 Solving -17 + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + -4x = 0 + 17 Combine like terms: -17 + 17 = 0 0 + -4x = 0 + 17 -4x = 0 + 17 Combine like terms: 0 + 17 = 17 -4x = 17 Divide each side by '-4'. x = -4.25 Simplifying x = -4.25Subproblem 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 = {-4.25, 3}
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