Question

How do you solve ${x^2} - 14x = 0$?

Answer 1

Hint: This equation is the quadratic equation. The general form of the quadratic equation is $a{x^2} + bx + c = 0$. Where ‘a’ is the coefficient of ${x^2}$, ‘b’ is the coefficient of x and ‘c’ is the constant term.
To solve this equation, we will apply the sum-product pattern. During the simplification, we will take out common factors from the two pairs. Then we will rewrite it in factored form.
 Therefore, we should follow the below steps:
> Apply sum-product pattern.
> Make two pairs.
> Common factor from two pairs.
>Rewrite in factored form.

Complete step-by-step answer:
Here, the quadratic equation is
$ \Rightarrow {x^2} - 14x = 0$
Let us apply the sum-product pattern in the above equation.
But, here the constant term is 0. So, we can directly take out x common to both terms of the left-hand side.
Therefore,
$ \Rightarrow x\left( {x - 14} \right) = 0$
Now, equate both the factors to zero to obtain the solution.
For the first factor:
$ \Rightarrow x = 0$
And for the second factor:
$ \Rightarrow x - 14 = 0$
Let us add 14 on both sides.
$ \Rightarrow x - 14 + 14 = 0 + 14$
By simplifying the above step,
$ \Rightarrow x = 14$

Hence, the solutions of the given quadratic equation are 0 and 14.

Note:
One important thing is, we can always check our work by multiplying out factors back together, and check that we have got back the original answer.
In the above question, we get the solutions x=0 and x=14.
So, $ \Rightarrow x = 14$
$ \Rightarrow x - 14$
To check our factorization, multiplication goes like this:
$ \Rightarrow x\left( {x - 14} \right) = 0$
Let us apply multiplication to remove brackets.
$ \Rightarrow {x^2} - 14x = 0$
Hence, we get our quadratic equation back by applying multiplication.
Here is a list of methods to solve quadratic equations:
> Factorization
> Completing the square
> Using graph
> Quadratic formula