How do you solve $9x^2 -18x - 1 =0$ by completing the square?

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Answer 1 · 2016-04-06T12:40:54

The solutions are:
$color(green)(x = (sqrt 10 + 3)/3$ , $color(green)(x = (-sqrt 10 + 3) / 3$

$9x^2 - 18x - 1 = 0$

$9x^2 - 18x = 1$

To write the Left Hand Side as a Perfect Square, we add 9 to both sides:

$9x^2 - 18x + 9 = 1 + 9$

$(3x)^2 - 2 * 3x * 3 + 3 ^2 = 10$

Using the Identity $color(blue)((a-b)^2 = a^2 - 2ab + b^2$ , we get

$(3x - 3)^2 = 10$

$3x - 3 = sqrt 10$ or $3x - 3 = -sqrt10$

$color(green)(x = (sqrt 10 + 3)/3$ or $color(green)(x = (-sqrt 10 + 3) / 3$

How do you solve 9x^2 -18x - 1 =09x^2 -18x - 1 =0 by completing the square?