X² - 4x - 12=0

solve by completing the square

x = - 2 0r x = 6

Step-by-step explanation:

from the question

X² - 4x - 12=0

solve by completing the square method

we have;

X² - 4x - 12=0

X² - 4x = 12

to make the left hand side a perfect square we add 4 to both sides.

X² - 4x + 4 = 12 + 4

X² - 4x + 4 = 16

from left hand side X² - 4x + 4

= (x - 2) * (x - 2)

it can be simply expressed as

(x-2) ²

so since X² - 4x + 4 has been simplified to be (x-2) ²

then,

(x-2) ² = 16

x - 2 = √ 16

since square root has two values it can either be positive or negative

so we have

x = 2 + √16

or

x = 2 - √16

therefore

x = 2 + √16

x = 2 + 4

x = 6

0r

x = 2 - 4

x = - 2