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

User Iain Brown
by
8.7k points

1 Answer

1 vote

Answer:

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

User Ritesh  Karwa
by
7.9k points

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