Question

How do you solve $ - 5{{\text{x}}^2} = - 500$?

Answer 1

Hint: In this question they have given a simple equation and asked to find ${\text{x}}$ . We have to solve this equation by transferring methods, first we need to separate the variables and the constants by transferring $ - 5$ to the other side and then find the square root of the obtained value. Finally we get the required answer.

Complete step-by-step solution:
The given equation is$ - 5{{\text{x}}^2} = - 500$,
First of all, we need to transfer $ - 5$ to the right hand side to separate the ${{\text{x}}^2}$ from its coefficient,
$ \Rightarrow - 5{{\text{x}}^2} = - 500$
Transferring $ - 5$ to the other side,
$ \Rightarrow {{\text{x}}^2} = \dfrac{{ - 500}}{{ - 5}}$
The signs get cancelled and by dividing we get,
\[ \Rightarrow {{\text{x}}^2} = 100\]
Now we have to take the square root of the obtained number i.e., $100$
$ \Rightarrow {\text{x = }}\sqrt {100} $
We know that ${10^2} = 100 = {-10^2}$

Therefore x=10 and -10 is the required answer.

Note: Students may face problem in finding the square root in almost all the cases,
This is a shortcut to find the square root of any real number. If you have to find the square root for any number, find its factors and split the terms as many as possible and take those numbers which are in doubles out of the square root.
Let us assume an example,
To find the square root of $144$ we can simply split the numbers by its factor,
$ \Rightarrow \sqrt {144} = \sqrt {2 \times 72} $
Now again,
$ \Rightarrow \sqrt {144} = \sqrt {2 \times 2 \times 36} $
So here we have two $2$ inside the square root thus we can take it out and then it becomes,
$ \Rightarrow \sqrt {144} = 2\sqrt {36} $
Again splitting the terms by its factors we get,
$ \Rightarrow \sqrt {144} = 2\sqrt {3 \times 3 \times 4} $
We can now take $3$ out as there as in doubles,
$ \Rightarrow \sqrt {144} = 2 \times 3\sqrt 4 $
Again splitting it,
$ \Rightarrow \sqrt {144} = 6\sqrt {2 \times 2} $
And it becomes
$ \Rightarrow \sqrt {144} = 6 \times 2$
On multiply we get,
$ \Rightarrow \sqrt {144} = 12$
We get the answer.