How do you solve (x-2)^2-25=0?

3 Answers
Deepak G.
Aug 24, 2016

x=7

x=-3

Explanation:

(x-2)^2-25=0

or

(x-2)^2=25

or

x-2=sqrt25

or

x-2=+-5

or

x=2+-5

or

x=2+5

or

x=7---------------------------------Ans 1

or

x=2-5

or

x=-3-----------------------------Ans 2

Jim G.
Aug 24, 2016

x=7,x=-3

Explanation:

First step is to isolate the (x-2)^2 term

add 25 to both sides.

rArr(x-2)^2-cancel(25)+cancel(25)=0+25

rArr(x-2)^2=25

now take the color(blue)"square root of both sides"

sqrt((x-2)^2)=+-sqrt25

rArrx-2=+-5

solve : x-2=5rArrx=5+2=7

solve : x-2=-5rArrx=-5+2=-3

Shwetank Mauria
Aug 24, 2016

x=7 or x=-3

Explanation:

We can use identity (a^2-b^2)=(a-b)(a+b). As such

(x-2)^2-25=0

hArr(x-2)^2-5^2=0

or (x-2-5)(x-2+5)=0

or (x-7)(x+3)=0

i.e. x=7 or x=-3

Related questions
See all questions in Use Square Roots to Solve Quadratic Equations
Impact of this question
10660 views around the world
You can reuse this answer
Creative Commons License