How do you solve using the completing the square method $x^{2} - 6 x - 16 = 0$ $x^2 - 6x - 16=0$ ?

Question

1377 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-03-22T17:40:01

The solutions are:
$x = 8$ $x = 8$ and
$x = - 2$ $x = -2$

$x^{2} - 6 x - 16 = 0$ $x^2 - 6x - 16=0$

$x^{2} - 6 x = 16$ $x^2 - 6x = 16$

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

$x^{2} - 6 x + 9 = 16 + 9$ $x^2 - 6x + color(blue)(9)= 16+ color(blue)(9)$

$x^{2} - 2 \cdot x \cdot 3 + 3^{2} = 25$ $x^2 - 2*x*3 + 3^2 = 25$

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

${(x - 3)}^{2} = 25$ $(x-3)^2 = 25$

$x - 3 = \sqrt{25}$ $x - 3 = sqrt 25$ or $x - 3 = - \sqrt{25}$ $x -3 = -sqrt25$

$x = 5 + 3 = 8$ $x = 5 + 3 = 8$ or $x = - 5 + 3 = - 2$ $x = -5 + 3 = -2$

The solutions are:
$x = 8$ $x = 8$ and
$x = - 2$ $x = -2$

How do you solve using the completing the square method x2−6x−16=0x^2 - 6x - 16=0?