Question

How do you solve ${{x}^{2}}+4x-5=0$ by completing the square?

Answer 1

Hint: The given question can be answered by performing the completing square method that is by expressing the given equation ${{x}^{2}}+4x-5=0$ in the form of ${{\left( x+a \right)}^{2}}-b=0$ and further simplifying it we will obtain the solutions.

Complete step by step answer:
For answering this question we need to solve the given equation ${{x}^{2}}+4x-5=0$ by using the completing the square method.
The completing square method is the process of solving quadratic equations by writing them in the form of ${{\left( x+a \right)}^{2}}-b=0$ .
For this equation ${{x}^{2}}+4x-5=0$ it can be expressed as ${{\left( x+2 \right)}^{2}}-9=0$.
By further simplifying this we will have
$\begin{align}
  & {{\left( x+2 \right)}^{2}}-9=0 \\
 & \Rightarrow {{\left( x+2 \right)}^{2}}=9 \\
\end{align}$ .
By performing some arithmetic calculations this expression can be further simplified as $x+2=\pm 3$.
After performing the simplifications we will have $x=-2\pm 3$ .
From this we will have $x=-5,1$ .

Hence we can conclude that the solutions of the given expression ${{x}^{2}}+4x-5=0$ are $-5$ and $1$

Note: We should be carefully performing the calculations while answering this question. This question can be answered in another method but we do not prefer it here because we are asked to do it by completing the square method. The other process is done by using the formulae for the equation $a{{x}^{2}}+bx+c=0$ is given by $\dfrac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a}$ . By using this formula for the expression ${{x}^{2}}+4x-5=0$ we will have $\dfrac{-4\pm \sqrt{{{4}^{2}}-4\left( -5 \right)}}{2}=\dfrac{-4\pm \sqrt{16+20}}{2}=\dfrac{-4\pm 6}{2}=-5,1$ . We had got the same answer in both the methods. Hence we can say that anyone can use anyone of the two methods for answering this question if not specified.