9x^(2)-18x+5=0 solve by completing the square

Answer 1

9x^2 -18x + 5 = 0

9(x^2 -2x + ) = -5

add half of 2, squared, times 9, to both sides: 9(-2/2)^2 = 9(1)=9

9(x^2 -2x +1) = -5 +9

9(x-1)^2 = 4

(x-1) ^2 = 4/9

take the square root of both sides

x-1 = +/-sqr(4/9)= +/-2/3

x-1 = +/- 2/3

x = 1 +/-2/3

x = 1-2/3, 1+2/3

x = 1/3, 5/3

check the answers

9x^2 -18x +5 =0

plug in x=1/3

9(1/3)^2 -18(1/3)+5

=9(1/9)-6 +5

=1-6+5

=0

plug in x=5/3

9(5/3)^2 -18(5/3)+5

=9(25/9) -30+5

=25 -30 +5

=0