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?

Answer: The factorization is given by x2+25 = (x-5i)(x+5i), where i = √-1 is an imaginary complex number.

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?

Answer: The solutions of x2+25 = 0 are 5i, -5i where i = √-1 is an imaginary complex number.

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:

ALSO READ:

Solve x⁴+x²+1=0

FAQs