Question

x² + 8x + 9 = 0

Answer 1

Given: x² + 8x + 9 = 0

$\Rightarrow$ x² + 8x = –9 …(1)

We make L.H.S. a perfect square by using

Third term = .${\left(\frac{1}{2}\times \mathrm{coefficient}\mathrm{of}x\right)}^2={\left(\frac{1}{2}\times 8\right)}^2=4^2=16$

On adding 16 to both sides of equation (1), we get:

x² + 8x + 16 = –9 + 16

$\Rightarrow$x² + 2 × x × 4 + (4)² = 7

$\Rightarrow$(x + 4)² = ${\left(\sqrt{7}\right)}^2$

On taking square root of both sides, we get:

$$\begin{gathered} x+4=\pm \sqrt{7} \\ \Rightarrow x=-4\pm \sqrt{7} \end{gathered}$$