Question

How do you solve $9{{r}^{2}}-3=-152$ ?

Answer 1

Hint: At first, we add $3$ to both the sides of the equation. Then, we divide the both sides of the equations by $9$ . We get an equation something like ${{r}^{2}}=-\dfrac{149}{9}$ . This can be written as ${{r}^{2}}=\dfrac{149}{9}{{i}^{2}}$ . The solution will then be $r=\pm i\sqrt{\dfrac{149}{9}}$

Complete step by step solution:
In the mathematical world, we come across what we call equations. Equations are nothing but statements that put forward the notion that two mathematical expressions are the same. Equations can be of various types. Equations can have no variables at all, may have one variable, or can even have multiple variables. The first type basically states the identity relation for example, $2=2$ . The second type says that the expression of a variable is equivalent to a number, for example ${{x}^{2}}+3x=5$ . The third type is called the equation of a curve or a straight line for example $x+y=1$ .
In the problem, the given equation that we have is,
$9{{r}^{2}}-3=-152$
We can see that the equation has only one variable, which is r over here. Also, the variable lies only on one side of the equation (the left-hand side to be precise). Thus, the equation falls in the second category of equations. We need to solve the given equation. By solving, we mean to find the value of r from the given equation. We do this by first adding $3$ o both sides of the equation and get,
$\begin{align}
  & \Rightarrow 9{{r}^{2}}=-149 \\
 & \Rightarrow {{r}^{2}}=-\dfrac{149}{9} \\
\end{align}$
Here, a square term is equal to a negative term. This is nothing but a problem of the imaginary world. The solution will be,
$\begin{align}
  & \Rightarrow {{r}^{2}}=-\dfrac{149}{9} \\
 & \Rightarrow r=\pm i\sqrt{\dfrac{149}{9}} \\
\end{align}$

Therefore, we can conclude that the solution for the equation is $r=\pm i\sqrt{\dfrac{149}{9}}$

Note: The given problem was not even a problem of quadratic equations. It required mostly the knowledge of complex numbers. Students may at first get confused with seeing the square term getting equal to a negative number. We must implement the concept of complex numbers here in order to get through the problem.