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

Question

Eli Assouline · Accepted Answer

Start by factorizing.

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#

Abigail Allen · Answer

#x = +- 5#

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#

Savannah Anderson · Answer

undefined To solve the equation 5x^2 - 125 = 0, first, add 125 to both sides to isolate the quadratic term:

5x^2 = 125

Then, divide both sides by 5 to solve for x^2:

x^2 = 25

Now, take the square root of both sides:

x = ±√25

Simplify:

x = ±5

So, the solutions to the equation 5x^2 - 125 = 0 are x = 5 and x = -5.