Question

Write x2 + 8x + 5 in the form (x+a)2 + b where a and b are integers.
a =
b=

Answer 1

`(x+4)^2 - 11 = 0\\`

a = 4

b = -11

Explanation:

`x^(2) +8x+5\\`

use the complete the square method:

`x^(2) +8x+5=0\\x^(2) +8x = -5\\\\(x+4)^(2) = x^2 + 8x + 16\\\\x^2 + 8x + 16 = -5 + 16\\`

we completed the square of x^2 + 8x + ... which is x^2 + 8x + 16 using (x+4)^2

we added 16 to both sides because whatever you do to one side, you have to do to the other:

`x^(2) +8x+16 = 11\\(x+4)^2 = 11\\(x+4)^2 - 11 =0`