Question

solve the quadratic equation by completing square
3p²+7p+1=0​

Answer 1

$\sf{\large{\underline{\underline{EXPLANATION:}}}}$

★Given,,

$\sf{3p^{2}+7p+1=0}$

★Now,, Using complete square method,,

$\sf{\implies{(\sqrt{3}p)^{2}+2\times{\sqrt{3}p}\times{\frac{7}{2\sqrt{3}}+(\frac{7}{2\sqrt{3}})^{2}}+1=(\frac{7}{2\sqrt{3}})^{2}}}$

$\sf{\implies{(\sqrt{3}p+\frac{7}{2\sqrt{3}})^{2}=(\frac{7}{2\sqrt{3}})^{2}-1}}$

$\sf{\implies{(\sqrt{3}p+\frac{7}{2\sqrt{3}})^{2}=\frac{49}{12}-1}}$

$\sf{\implies{(\sqrt{3}p+\frac{7}{2\sqrt{3}})^{2}=\frac{49-12}{12}}}$

$\sf{\implies{(\sqrt{3}p+\frac{7}{2\sqrt{3}})^{2}=\frac{37}{12}}}$

$\sf{\implies{\sqrt{3}p+\frac{7}{2\sqrt{3}}=\pm\sqrt{\frac{37}{12}}}}$

$\sf{\implies{\sqrt{3}p=\frac{7}{2\sqrt{3}}\pm\{\frac{\sqrt{37}}{2\sqrt{3}}}}$

$\sf{\implies{\sqrt{3}p=\frac{7\pm\sqrt{37}}{2\sqrt{3}}}}$

$\sf{\implies{p=\frac{7\pm\sqrt{37}}{2\sqrt{3}\times{\sqrt{3}}}}}$

$\sf{\implies{p=\frac{7\pm\sqrt{37}}{6}}}$

★Therefore,,

$\sf{\implies{p=\frac{7+\sqrt{37}}{6}\:\:or\:\frac{7-\sqrt{37}}{6}}}$

$\rule{200}2$

Hope it helps ❣️❣️❣️