Question

Find the roots of the following quadratic equation, if they exist, by the method of completing the square:

x² + 5 = -6x

Answer 1

The given Q.E. is x² + 5 = -6x 

⇒ x² + 6x = -5 

⇒ (x)² + 2.(x).3 = -5 

Now L.H.S. is of the form a² + 2ab where b = 3. 

Adding b² = 3² on both sides we get 

x² + 2(x)(3) + 3² = -5 + 3² 

(x + 3)² = -5 + 9 = 4 

∴ x + 3 = 74 = ± 2 

⇒ x = +2 – 3 or – 2 – 3 

\(\therefore\) x= -1 or -5 are the roots of the given Q.E.