How do you solve x^2-6x-9=0 by completing the square?

2 Answers
LM
Jan 19, 2018

(x-3)^2-18

Explanation:

x^2-6x-9 = (x^2-6x+9)-18

x^2-6x+9 = (x-3)(x-3) = (x-3)^2

(x-3)^2-18 = (x^2-6x+9)-(9+9) = x^2-6x+9-9-9

= x^2-6x-9

George C.
Jan 19, 2018

x = 3+-3sqrt(2)

Explanation:

The difference of squares identity can be written:

A^2-B^2 = (A-B)(A+B)

Use this with A=(x-3) and B=3sqrt(2) as follows:

0 = x^2-6x-9

color(white)(0) = x^2-2(x)(3)+3^2-18

color(white)(0) = (x-3)^2-(3sqrt(2))^2

color(white)(0) = ((x-3)-3sqrt(2))((x-3)+3sqrt(2))

color(white)(0) = (x-3-3sqrt(2))(x-3+3sqrt(2))

Hence:

x = 3+-3sqrt(2)

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