Question

x
$x ^{2} - 49x = 0$
​

Answer 1

To solve the equation, we can use the following:-

• Quadratic Formula
• Complete the Square
• Factorization

Here I am going to use the factorization method.

It is a binomial. As you see there's a common factor.

$\sf{\to (x)\times (x)-49\times (x)}$

$\sf{\to x(x-49)}$

Now it will have two roots at:-

• $\sf{x=0}$
• $\sf{(x-49)=0}$

Therefore, two roots are $\sf{x=0\:or\:x=49}$.

Extra Information

1. Sometimes there are some problems that aren't solved by factorization.

Then we could use the followings:

• Quadratic Formula
• Complete the Square

2. The quadratic formula was actually derived from complete the square method.

3. Around 300 BC, Babylonians were the first to solve the quadratic equations.