Question

How do you solve $\dfrac{2}{3}{x^2} = 24$?

Answer 1

Hint: According to the question we have to solve the given expression $\dfrac{2}{3}{x^2} = 24$which is as mentioned in the question. So, first of all to determine the solution or we can say to determine the value of x or the roots/zeros of the quadratic expression we have to multiply with 3 in the both sides of the given quadratic expression.
Now, we have to divide by 2 in the both sides of the expression as obtained after multiplying with the integer 3.
Now, we have to determine the values of the variable x which can determined with the help of the formula as mentioned below:

Formula used:
$
x = \sqrt {{a^2}} \\
x = \pm a....................(A) \\
 $

Complete step by step solution:
Step 1: First of all to determine the solution or we can say to determine the value of x or the roots/zeros of the quadratic expression we have to multiply with 3 in the both sides of the given quadratic expression. Hence,
$
   \Rightarrow 3 \times \dfrac{2}{3}{x^2} = 24 \times 3 \\
   \Rightarrow 2{x^2} = 72 \\
 $
Step 2: Now, we have to divide by 2 in the both sides of the expression as obtained after multiplying with the integer 3. Hence,
$
   \Rightarrow \dfrac{{2{x^2}}}{2} = \dfrac{{72}}{2} \\
   \Rightarrow {x^2} = 36 \\
 $
Step 3: Now, we have to determine the values of the variable x which can be determined with the help of the formula (A) as mentioned in the solution hint. Hence,
$
   \Rightarrow x = \sqrt {36} \\
   \Rightarrow x = \pm 6 \\
 $

Hence, with the help of the formula (A) as mentioned in the solution hint we have determined the solution of the given expression which is $x = \pm 6$.

Note:
1) To obtain the required solution or the roots/zeros of the given expression it is necessary that we have to multiply the whole expression with 3 and then divide the whole expression with 2.
2) On solving a quadratic expression only two possible roots/zeroes can be obtained which will satisfy the given quadratic expression mean on placing these in place of x the whole expression becomes 0.