Question

Solve the equation 2xsquare +13x+15=0 by formula method , completing square method and factorizsation method.

Answer 1

above r all method to solve equation

n roots r -3/2,-5

Answer 2

$2 {x}^{2} - 13x + 9 = 0$

$move \: consonant \: to \: right - hand \: side \: and \: change \: its \: sign$

$2 {x}^{2} - 13x = \red{ - 9}$

$divide \: both \: side \: eq. \: by2$

$\red{ {x}^{2} - \frac{13}{2} x = \frac{ - 9}{2} }$

$add \: ( \frac{13}{4} {)}^{2} to \: both \: side \: eq.$

${x}^{2} - \frac{13x}{2} \red{+ (\frac{13}{4})^{2} } = - \frac{9}{2} \red { + ( \frac{13}{4} {)}^{2} }$

$using \: {a}^{2} - 2ab + {b}^{2} = (a - {b)}^{2} factor \: the \: eq.$

$\red{(x - \frac{13}{4} {)}^{2} } = - 9 + ( \frac{13}{4} {)}^{2}$

${(x - \frac{13}{4} {)}^{2} } = \red{ \frac{97}{16} }$

$solve \: eq. \: for \: x$

$\red{x = \frac{ - \sqrt{97} + 13}{4} }$

$\red{x = \frac{ \sqrt{97} + 13}{4} }$

$the \: eq. \: has \: 2 \: sol.$

$\boxed{ \pink{x = \frac{ - \sqrt{97} + 13}{4} }}$

${\boxed {\orange{{{x = \frac{ \sqrt{97} + 13}{4} }}}}}$