Question

How do you solve \[{{x}^{2}}-4=5\]?

Answer 1

Hint: In this problem, we have to solve and find the value of the given equation. We can see that the given equation is a perfect square equation. We can first add the number 4 on both sides in order to simplify the step, we can then take square root on both sides, to cancel the square term and to get the value of x.

Complete step-by-step answer:
We know that the given equation to be solved is,
\[{{x}^{2}}-4=5\]
We can now simplify the given equation to solve for x.
We know that to simplify the equation we can add or subtract similar numbers in the both left-hand side and the right-hand side of the equation.
We can now add the number 4 on both left-hand side and the right-hand side of the given equation, we get
\[\Rightarrow {{x}^{2}}-4+4=5+4\]
We can now simplify the above step we get,
\[\Rightarrow {{x}^{2}}=9\]
We can now take square root on both left-hand side and the right-hand side of the given equation, we get,
\[\Rightarrow \sqrt{{{x}^{2}}}=\pm \sqrt{9}\]
We can see that on the left hand we can cancel the square root and the square and we can simplify the right-hand side, we get
\[\begin{align}
  & \Rightarrow x=\pm \sqrt{{{3}^{2}}} \\
 & \Rightarrow x=3,-3 \\
\end{align}\]
Therefore, the value of x = 3, -3.

Note: Students make mistakes while writing the plus or minus symbol, as we should write it while taking square root on both sides. We should also remember that real numbers obtained in the result as the given equation is a perfect square equation, otherwise it would result in a complex number.