# How to Factorise x^2+25 | Solve x^2+25=0

In this post, we will learn how to factorise the quadratic algebraic expression x2+25, then solve the quadratic equation x2+25=0.

## How to Factorise x2+25?

Solution:

To factorise the expression x2+25, we first write the expression in the form of a2-b2. This can be done as follows:

x2+25

= x2 – (-25) as the negative of negative x is the number x itself.

= x2 – (-1 × 25)

= x2 – 25i2 where i = √-1

= x2 – (5i)2

= (x-5i) (x+5i) using the formula a2-b2 = (a-b)(a+b).

So the factors of x2+25 is as follows: x2+25 = (x-5i)(x+5i).

## How to Solve x2+25=0?

Solution:

Method 1: In the first method, we will solve the equation x2+25 = 0 by factorization. The factorization of x2+25 is given above.

x2+25 = 0

⇒ (x-5i)(x+5i) = 0

So either x-5i=0 or x+5i =0

⇒ Either x=5i or x= -5i

So the solutions of x2+25 = 0 are x=5i, -5i and thus there are two solutions of the equation x2+25 = 0.

Method 2: Next, we will find the solutions of x2+25 = 0 by the square root method.

x2+25 = 0

⇒ x2 = -25

Taking square root on both sides, we get that

x = ± $\sqrt{-25}$ = ± $\sqrt{25 \times (-1)}$ = ± $\sqrt{25 \times i^2}$ as $i=\sqrt{-1}$.

⇒ x = ± 5i

⇒ x= 5i, -5i.

So 5i and -5i are the solutions of the given equation x2+25=0.

Video Solution of x2+25=0:

Solve x4+x2+1=0

## FAQs

Q1: How to factor x2+25?