# Chapter 10 - Radical Expressions and Equations - 10-2 Simplifying Radicals - Practice and Problem-Solving Exercises - Page 611: 71

$1 ± \sqrt 5$

#### Work Step by Step

The trinomial cannot be factored so we use the quadratic formula to calculate the x. $x= \frac{-b ± \sqrt (b^{2} - 4ac)}{2a}$ $n^{2} - 2n - 4$ In this trinomial a = 1, b= -2 and c= -4 $x= \frac{-(-2) ± \sqrt (-2^{2} - 4(1)(-4))}{2(1)}$ $x= \frac{2 ± \sqrt (4 + 16)}{2}$ We add the 4 and 16 together $x= \frac{2 ± \sqrt (20)}{2}$ Square root of 20 is $2\sqrt 5$ because the factors of 72 are 4 and 5 and 4 is a perfect square of 2. $x= \frac{2 ± 2\sqrt 5}{2}$ We simplify the numbers to get the final x value. $n= 1 ± \sqrt 5$

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