Question

19) n? – 8n – 27 = 6 solve each equation by completing the square

Answer 1

Answer:

n=11 or n=-3

Step-by-step explanation:

Consider the quadratic equation $n^2-8n-27=6.$

First, remind the formula

$(a-b)^2=a^2-2ab+b^2$

To complete the square, note that

$8n=2\cdot n\cdot 4$

Hence, we need $+4^2$

Add 16 to both sides of equation:

$n^2-8n+16-27=6+16\\ \\(n-4)^2-27=22\\ \\(n-4)^2=49\\ \\n-4=7\text{ or }n-4=-7\\ \\n=11\text{ or }n=-3$