Question

How do you solve the equation $3({x^2} + 2) = 18?$

Answer 1

Hint: First of all move the term multiplicative on one side to the opposite side which goes to the denominator. Then make the required term “x” the subject and simplify for the required value.

Complete step by step solution:
Take the given expression: $3({x^2} + 2) = 18$
Term multiplicative on one side, if moved to the opposite side then it goes to the denominator.
$ \Rightarrow ({x^2} + 2) = \dfrac{{18}}{3}$
Find the factors for the numerator on the right hand side of the equation –
$ \Rightarrow ({x^2} + 2) = \dfrac{{6 \times 3}}{3}$
Common factors from the numerator and the denominator cancels each other. Therefore, remove from the numerator and the denominator.
$ \Rightarrow ({x^2} + 2) = 6$
Now, move the constant on the opposite side. When you move any term from one side to the other, the positive term becomes negative and vice-versa.
$ \Rightarrow {x^2} = 6 - 2$
Simplify the above expression –
$ \Rightarrow {x^2} = 4$
Take square-root on both the sides of the equation –
$ \Rightarrow \sqrt {{x^2}} = \sqrt 4 $
Square and square-root cancel each other on the left hand side of the equation –
$ \Rightarrow x = \pm 2$
This is the required solution.

Thus the required solution is $ x = \pm 2$.

Note: Be careful about the sign convention, when you move any term from one side to the other the sign of the term also changes. Positive terms become negative and the negative term becomes positive. Also, remember the square of positive and the negative term gives a result always as positive and square root of the positive term can give negative or positive terms.