(x- 5/2) ^2 = 9/4?

[07]
(x-5/2)^2=9/4
x-5/2=+-3/2 [square-rooting both sides]
x=5/2+-3/2
=4 or 1

(x - 5/2) = ± (3/2)
x = 5/2 ± (3/2)
x = 4 , x = 1

Square root both sides.

x - 5/2 = 3/2. x - 5/2 = -3/2.
x = 4 x = 1.

Find x:
(x - 5/2)² = 9/4
x - 5/2 = 3/2
x = 5/2 + 3/2
x = 8/2 or 4

Answer: x = 4

Proof (substitute x with 4):
(4 - 5/2)² = 9/4
(8/2 - 5/2)² = 9/4
(3/2)² = 9/4
9/4 = 9/4

sqrt((x-5/2)^2) = sqrt(9/4)
x-5/2 = (sqrt 9)/(sqrt 4)
x - 5/2 = 3/2
x = 3/2 + 5/2
x = 8/2
x = 4

Hi.... =D

(x-5/2)(x-5/2) = 9/4
(x^2 - 5x + 25/4) = 9/4
x^2 - 5x +16/4 = 0
x^2 - 5x + 4 = 0
(x - 4) (x-1) = 0
x = 4.00 ; x=1.00

Rewrite

(X - 2.5) ^2 = 2.25

Now get rid of the square by multipling (x-2.5) by itself.

X^2 - 5x + 6.25 = 2.25

Move everything to the Left.

X^2 - 5x + 4 = 0

Factor it out

(X-4) (X-1) = 0

So

X = 4 or X = 1

(x - 5/2)^2 = 9/4
(x - 5/2)(x - 5/2) = 9/4
x^2 - 5x/2 - 5x/2 + 25/4 = 9/4
x^2 - 10x/2 = 9/4 - 25/4
x^2 - 10x/2 = -16/4
x^2 - 10x/2 + 16/4 = 0
x^2 - 5x + 4 = 0
(x - 1)(x - 4) = 0

x - 1 = 0
x = 1

x - 4 = 0
x = 4

∴ x = 1 or 4