Question

If the quadratic equation x2 + 6x + 19 = 0 is rewritten in the form (x - p)2 = q ,

what is the value of p and q

Answer 1

p = -3

q = -10

Explanation:

`x^(2)+6x+19=x^(2)+6x+9+10`

`\text{we know that} \ x^(2)+6x+9=\left (x+3)^2\right\ \text{ because it is a special product}`

`\text therefore \ ,\ x^(2)+6x+19=(x + 3)^2+10`

`\text therefore \ ,\ x^(2)+6x+19=0 \ means\ (x + 3)^2= -10\ means\ (x -\ - 3)^2= -10`