How do you solve \[7{x^2} = - 21\] ?

Hint: Given is an equation with one variable. We have to find the value of that variable. First we will separate the variables and constants. Then we will perform the operations of constants and then find the root of x to find the value of x. Also \[\sqrt { - 1} = i\] will simplify the answer that is imaginary number \[i\]

Complete step-by-step answer:
Given that
 \[7{x^2} = - 21\]
Taking 7 on RHS we get,
 \[ \Rightarrow {x^2} = \dfrac{{ - 21}}{7}\]
Now divide 21 by 7 we get,
 \[ \Rightarrow {x^2} = - 3\]
Taking root on both sides we get,
 \[ \Rightarrow x = \sqrt { - 3} \]
Now we know that \[\sqrt { - 1} = i\] that is imaginary number
Thus we can write,
 \[ \Rightarrow x = \sqrt {3 \times - 1} \]
Putting the value of \[\sqrt { - 1} = i\]
 \[ \Rightarrow x = \sqrt 3 i\]
This is our answer.
So, the correct answer is “ \[ x = \sqrt 3 i\] ”.

Note: Note that we cannot remove the minus sign directly whereas -3 can be written as \[\sqrt {3 \times - 1} \] . And then -1 is replaced by an imaginary number. But also note that \[{i^2} = - 1\] so when we write \[i\] we write it outside the root. That is \[\sqrt 3 i\] and not \[\sqrt {3i} \] , both are different. In multiple choice questions you may come across these types of tricky options. This imaginary number is also known as complex number of the form \[z = x + iy\] , where x is the real part of the number and y is the imaginary part of the number.