Question

Solve by completing the square.

Answer 1

Option D is correct, i.e. {1, -17}.

Explanation:

Given the problem is n² + 16n = 17.

Comparing it with general form of Perfect Square i.e. x² + 2ax + a² = (x+a)².

We can write it as follows:-

n² + 2*8n = 17

Adding 8² on both sides,

n² + 2*8n + 8² = 17 + 8²

(n+8)² = 17 + 64 = 81

n+8 = √81 = ±9

n+8 = 9 or n+8 = -9

n = 9-8 or n = -9-8

n = 1 or n = -17

Hence, option D is correct, i.e. {1, -17}.

Answer 2

Option D. {1,-17}

Explanation:

n^2+16n=17

n^2+16n+(16/2)^2=17+(16/2)^2

n^2+2n(8)+(8)^2=17+(8)^2

(n+8)^2=17+64

(n+8)^2=81

sqrt[(n+8)^2]=+-sqrt(81)

n+8=+-9

n+8-8=+-9-8

n=+-9-8

n1=+9-8→n1=1

n2=-9-8→n2=-17

Solution: {1,-17}