How do you solve 5x^2 - 125 = 0?

2 Answers
Mar 13, 2018

Start by factorizing.

Explanation:

Start by factorizing

5(x^2 - 25) = 0

then you can divide both sides by 5 and since 0/5 =0 you get the expression:

x^2 - 25 = 0

rearrange so that 25 is on the right hand side

x^2 =25

x=± sqrt25

x=± 5

Mar 13, 2018

x = +- 5

Explanation:

To make progress, an attempt should be made to have just x on one side of the equation to see what it is equal to (on the other side of the equation).

By inspection, both 5 and -125 are divisible by 5. Zero is also divisible by 5 in the sense 0/5 = 0

So, dividing both sides of the equation by 5 (also called "dividing through by 5)

5x^2 - 125 = 0

implies

(5x^2)/5 - (125)/5 = 0/5

that is

x^2 - 25 = 0

Now 25 may be added to both sides to give

x^2 - 25 + 25 = 0 + 25

that is

x^2 = 25

You will recognise 25 as a perfect square so finding a solution should be easy but take care! Remember square numbers have two roots, a positive one and a negative one. So

x^2 = 25

implies

sqrt(x^2) = sqrt(25)

that is

x = 5
or
x = -5