x^2 - 6x
= x^2 - 6x + 9 - 9
= (x-3)^2 - 9
3x^2 + 20x
= 3(x^2 + (20/3)x + 100/9 - 100/9
= 3( (x + 10/3)^2 - 100/9
= 3(x+10/3)^2 - 100/3
Rewrite each of the following expressions as a difference of two squares by completing the square (e.g. x^2 + 4x is rewritten (x + 2)^2 - 4:
(a) x^2 - 6x
(b) 3x^2 + 20x
2 answers
divide 6 by 2 and square it, 9
x^2 - 6 x + 9 -9
(x-3)^2 - 3^2
3(x^2 + 20 x/3)
(10/3)^2 = 100/9
3 [ x^2 + 20/3 x + (10/3)^2 - (10/3)^2 ]
= 3 [ (x-10/3)^2 - (10/3)^2 ]
x^2 - 6 x + 9 -9
(x-3)^2 - 3^2
3(x^2 + 20 x/3)
(10/3)^2 = 100/9
3 [ x^2 + 20/3 x + (10/3)^2 - (10/3)^2 ]
= 3 [ (x-10/3)^2 - (10/3)^2 ]
1 answer