Question

Solve the given quadratic equation for x:-
\[{{x}^{2}}-7x-18=0\]

Answer 1

- Hint: In this question, we are asked to solve the given quadratic equation which means that we have to find the roots of this given quadratic equation and that can be done by using the quadratic formula which is as follows
\[roots=\dfrac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a}\]
(For a quadratic equation \[a{{x}^{2}}+bx+c=0\])

Complete step-by-step solution -

As mentioned in the question, we have to find the roots of the given quadratic equation.
Now the quadratic equation is as follows
\[{{x}^{2}}-7x-18=0\]
Now, on using the quadratic formula, we get the following result
\[\begin{align}
  & \left( roots=\dfrac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a} \right) \\
 & \Rightarrow {{x}^{2}}-7x-18=0 \\
 & \Rightarrow x=\dfrac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a} \\
 & \Rightarrow x=\dfrac{-(-7)\pm \sqrt{{{(-7)}^{2}}-4\times 1\times -18}}{2\times 1} \\
 & \Rightarrow x=\dfrac{7\pm \sqrt{49+72}}{2} \\
 & \Rightarrow x=\dfrac{7\pm \sqrt{121}}{2} \\
 & \Rightarrow x=\dfrac{7\pm 11}{2} \\
 & \Rightarrow x=\dfrac{7+11}{2},\dfrac{7-11}{2} \\
 & \Rightarrow x=\dfrac{18}{2},\dfrac{-4}{2} \\
 & \Rightarrow x=9,-2 \\
\end{align}\]
Hence, the roots of the given quadratic equation are 9 and -2.

Note:- Two other methods with which we can solve a quadratic equation are as follows
Splitting the middle term
Completing the square
Both of these methods can be used to solve a quadratic equation and hence we can get the same solution by using them instead of the quadratic formula.