Question

How do you solve ${x^2} - 6x = 0$ ?

Answer 1

Hint: In this type of problems, first we need to rewrite the given expression(if necessary) in general form of quadratic equation given by: $a{x^2} + bx + c = 0$, now to find the roots we can make use of the quadratic formula given by: $x = \dfrac{{ - b \pm \sqrt {{b^2} - 4ac} }}{{2a}}$. So by making use of this formula we can easily solve the given expression.

Complete step by step answer:
Here in this question they have given an expression which is ${x^2} - 6x = 0$ to solve using quadratic formula.
The general or standard form of the quadratic equation is given by: $a{x^2} + bx + c = 0$ where $a,b,c$ are constant values. Now we need to rewrite the given expression in the general form.
Therefore, the given equation ${x^2} - 6x = 0$ can be written as
 ${x^2} - 6x + 0 = 0$ (Here the value of $c$ is not given which can be written as 0 for simplification purposes).
Now compare the equation ${x^2} - 6x + 0 = 0$ with the general form $a{x^2} + bx + c = 0$ we have $a = 1$ , $b = - 6$ and $c = 0$.
Now to find the roots of $x$ we can make use of the quadratic formula given by: $x = \dfrac{{ - b \pm \sqrt {{b^2} - 4ac} }}{{2a}}$.
Substitute the values $a = 1$ , $b = - 6$ and $c = 0$ in the above equation, we get
$x = \dfrac{{ - ( - 6) \pm \sqrt {{{( - 6)}^2} - 4 \times 1 \times 0} }}{{2 \times 1}}$
$ \Rightarrow x = \dfrac{{6 \pm \sqrt {36} }}{2}$ Here, $36$ can be written as ${6^2}$.
$ \Rightarrow x = \dfrac{{6 \pm \sqrt {{6^2}} }}{2}$
Square and square root get cancelled in the above expression, we get
$ \Rightarrow x = \dfrac{{6 \pm 6}}{2}$ Which is having two roots.
Now simplify for the roots of $x$ , we have
$ \Rightarrow x = \dfrac{{6 + 6}}{2}$ $ \Rightarrow x = \dfrac{{6 - 6}}{2}$

On simplifying the above expression, we get
$x = 6$ and $x = 0$ as the roots of the given equation ${x^2} - 6x = 0$

Note:
Whenever we have this type of problem we can easily find the roots by using the quadratic formula but you need to remember the formula correctly. Here the simplification part is a bit difficult but you can simplify step by step to get the correct answer.