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Simplifying (5x + 4)(5x + 4) = 81 Reorder the terms: (4 + 5x)(5x + 4) = 81 Reorder the terms: (4 + 5x)(4 + 5x) = 81 Multiply (4 + 5x) * (4 + 5x) (4(4 + 5x) + 5x * (4 + 5x)) = 81 ((4 * 4 + 5x * 4) + 5x * (4 + 5x)) = 81 ((16 + 20x) + 5x * (4 + 5x)) = 81 (16 + 20x + (4 * 5x + 5x * 5x)) = 81 (16 + 20x + (20x + 25x^{2})) = 81 Combine like terms: 20x + 20x = 40x (16 + 40x + 25x^{2}) = 81 Solving 16 + 40x + 25x^{2}= 81 Solving for variable 'x'. Reorder the terms: 16 + -81 + 40x + 25x^{2}= 81 + -81 Combine like terms: 16 + -81 = -65 -65 + 40x + 25x^{2}= 81 + -81 Combine like terms: 81 + -81 = 0 -65 + 40x + 25x^{2}= 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-13 + 8x + 5x^{2}) = 0 Factor a trinomial. 5((-13 + -5x)(1 + -1x)) = 0 Ignore the factor 5.## Subproblem 1

Set the factor '(-13 + -5x)' equal to zero and attempt to solve: Simplifying -13 + -5x = 0 Solving -13 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + -5x = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -5x = 0 + 13 -5x = 0 + 13 Combine like terms: 0 + 13 = 13 -5x = 13 Divide each side by '-5'. x = -2.6 Simplifying x = -2.6## Subproblem 2

Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1## Solution

x = {-2.6, 1}

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