How do you solve using the completing the square method $x^2 - 8x - 3 = 0$ ?

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Answer 1 · 2016-03-23T17:09:45

The solutions are:
$color(green)(x = sqrt 19 + 4$
$color(green)(x = -sqrt 19 + 4$

$x^2 - 8x - 3 = 0$

$x^2 - 8x = 3$

To write the Left Hand Side as a Perfect Square, we add 16 to both sides:

$x^2 - 8x + 16 = 3 + 16$

$x^2 - 2 * x * 4 + 4^2 = 19$

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

$(x-4)^2 = 19$

$x - 4 = sqrt19$ or $x -4 = -sqrt19$

$color(green)(x = sqrt 19 + 4$ or $color(green)(x = -sqrt 19 + 4$

How do you solve using the completing the square method x^2 - 8x - 3 = 0x^2 - 8x - 3 = 0?