Question

How do you solve the equation: $4{{x}^{2}}=20$?

Answer 1

Hint: We will divide both sides of the equation by a common factor of both terms. Then we will see the definition of a square root. We will obtain an equation with a square term on one side of the equation and a constant term on the other side of the equation. We will take the square root on both sides of the equation to obtain the solution of the given equation.

Complete step by step answer:
The given equation is $4{{x}^{2}}=20$. We can see that we can divide the term on the left hand side by 4. Also, we know that $4\times 5=20$. So, 4 is a factor of 20. Dividing both sides of the given equation by 4, we get the following,
$\begin{align}
  & \dfrac{4{{x}^{2}}}{4}=\dfrac{20}{4} \\
 & \therefore {{x}^{2}}=5 \\
\end{align}$
A square of a number is obtained by multiplying the number to itself. A square root of a number is defined to be the value that has the square as the given number.
We can see that in the above equation, we have the square of $x$ on the left hand side. Now, we will take the square root on both sides of the above equation. On the left hand side we have ${{x}^{2}}$. So, its square root is $x$. On the right hand side, we have the constant term, 5. The square root of 5 can be given as $\sqrt{5}$ since $\sqrt{5}\times \sqrt{5}=5$ or as $-\sqrt{5}$ since $-\sqrt{5}\times -\sqrt{5}=5$
Therefore, we get the following,
$x=\pm \sqrt{5}$

Note:
We should be familiar with the concept of squares and square roots for such types of questions. We can also shift the constant term to the left hand side and then factorize the quadratic equation. We can use algebraic identities or the methods to solve the quadratic equations. We should do the calculations explicitly to avoid making any errors.