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Simplifying (4x + 1)(x + 1) = 85 Reorder the terms: (1 + 4x)(x + 1) = 85 Reorder the terms: (1 + 4x)(1 + x) = 85 Multiply (1 + 4x) * (1 + x) (1(1 + x) + 4x * (1 + x)) = 85 ((1 * 1 + x * 1) + 4x * (1 + x)) = 85 ((1 + 1x) + 4x * (1 + x)) = 85 (1 + 1x + (1 * 4x + x * 4x)) = 85 (1 + 1x + (4x + 4x2)) = 85 Combine like terms: 1x + 4x = 5x (1 + 5x + 4x2) = 85 Solving 1 + 5x + 4x2 = 85 Solving for variable 'x'. Reorder the terms: 1 + -85 + 5x + 4x2 = 85 + -85 Combine like terms: 1 + -85 = -84 -84 + 5x + 4x2 = 85 + -85 Combine like terms: 85 + -85 = 0 -84 + 5x + 4x2 = 0 Factor a trinomial. (-21 + -4x)(4 + -1x) = 0Subproblem 1
Set the factor '(-21 + -4x)' equal to zero and attempt to solve: Simplifying -21 + -4x = 0 Solving -21 + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '21' to each side of the equation. -21 + 21 + -4x = 0 + 21 Combine like terms: -21 + 21 = 0 0 + -4x = 0 + 21 -4x = 0 + 21 Combine like terms: 0 + 21 = 21 -4x = 21 Divide each side by '-4'. x = -5.25 Simplifying x = -5.25Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {-5.25, 4}
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