Question

3p² + 4 = –7p

Answer 1

Given: 3p² + 4 = –7p
=>3p² + 7p = –4
On dividing both sides by 3, we get:
p² + $\frac{7}{3}$ p =$-\frac{4}{3}$… (1)
We make L.H.S. a perfect square by using
$$\begin{gathered} \mathrm{Third}\mathrm{term}={\left(\frac{1}{2}\mathrm{coefficient}\mathrm{of}\mathrm{p}\right)}^2={\left(\frac{1}{2}\times \frac{7}{3}\right)}^2={\left(\frac{7}{6}\right)}^2=\frac{49}{36} \\ \mathrm{On}\mathrm{adding}\frac{49}{36}\mathrm{to}\mathrm{both}\mathrm{sides}\mathrm{of}\mathrm{equation}\left(1\right),\mathrm{we}\mathrm{get}: \\ {p}^2+\frac{7}{3}p+\frac{49}{36}=-\frac{4}{3}+\frac{49}{36} \\ =>p^2+2\times p\times \frac{7}{6}+{\left(\frac{7}{6}\right)}^2=\frac{1}{36} \\ =>{\left(p+\frac{7}{6}\right)}^2={\left(\frac{1}{6}\right)}^2 \\ \text{T}\mathrm{aking}\mathrm{square}\mathrm{root}\mathrm{of}\mathrm{both}\mathrm{sides},\mathrm{we}\mathrm{get}: \\ p+\frac{7}{6}=\pm \frac{1}{6} \\ =>p=-\frac{7}{6}\pm \frac{1}{6}=\frac{-7\pm 1}{6} \\ =>p=\frac{-8}{6},\frac{-6}{6}=-\frac{4}{3},-1 \end{gathered}$$