Question

2x$2x^{2} +x-3=0$

Answer 1

$\Large\sf\underline{Given:}$

2x $\bf\color{black}{2x^{2}+x-3=0}$

$\large\sf\underline{To\:find:}$

$\sf\color{grey}{The\:value\:of\:x.}$

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

2x $\bf\color{black}{2x^{2}+x-3=0}$

$\bf\color{black}{●\:\: Multiplying\:by\: 2,\: So \:we \:get}$

$\bf{4x^{2}+2x-6=0}$

$\large\sf\underline{Using\: middle\:term\: breaking\: method:}$

In this method we are going to split the middle term such a way that when we multiply it should be equal to 4x6 i.e. 24 and when we subtract it should be equal to 2.

$\sf{4x^{2}+(6-4)x -6=0}$$\sf{4x^{2}+6x-4x-6=0}$$\sf{2x(2x+3)\:-2(2x-3)=0}$$\sf{(2x+3)\:(2x-2)=0}$

$\sf\color{grey}{Now\:,}$

$\sf{(2x+3)=0\:,\:(2x-2)=0}$$\sf{2x=-3\:\:\:\:,2x=2}$

$\tt\color{lightpink}{Hence,}$

$\tt\Large\color{teal}{x = \frac{ - 3}{2} \:and \:1}$

────────────★