please solve: (x-4)^2 = 36?

(x-4)^2 = 36

Since both sides are perfect squares,

Let's square root both sides.

sqrt((x-4)^2) = sqrt(36)

= positive and negative (x-4) = 6

We can equate both sides now, since it is in linear form.

For positive:
x-4 = 6

For negative:
-(x-4)=6
= -x+4 = 6

Transpose:

Positive:
x = 6+4

x = 10

Negative:

-x = 6-4

-x= 2

x = -2

***The value for x is 10 and -2

(x-4)(x-4) = 36

x^2 - 4x - 4x +16 = 36

x^2 - 8x +16 = 36

x^2 - 8x -20 = 0

(x - 10)(x + 2) = 0

x =10 or x = -2

Try them in the formula:

(10 - 4)^2 = 6^2 = 36

(-2 - 4)^2 = -6^2 = 36

36 X 4

x - 4 = ± 6
x = 4 ± 6
x = 10 , x = - 2

x - 4 = +6 or x - 4 = -6
x= 10 or x= -2

(x - 4) ^2 = 36
x - 4 = root(36)
[1] x - 4 = 6
--> x = 10

or

[2] x - 4 = -6
--> x = -6 + 4
--> x = -2


So there are two answers: x=10 and x=-2

(x-4)^2 = 36
(x - 4) = ±6
x = 4 ±6
x = -2 or 10

(x - 4) ^2 = 36
x - 4 = sqrt 36
x - 4 = 6 or -6
x = 10 or -2

(x - 4)^2 = 36
x - 4 = ±√36
x - 4 = ±6

x - 4 = 6
x = 6 + 4
x = 10

x - 4 = -6
x = -6 + 4
x = -2

∴ x = -2 , 10

(x-4)^2 = 36

sqrt both sides

x - 4 = 6

add 4 on both sides

x = 40