Question

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

Answer 1

n=11 or n=-3

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`