Question

2x²+5x-18=0 solve by factorisation method​

Answer 1

Answer:

$\large\boxed{\sf{x=2\;and\;x = -\dfrac{9}{2}}}$

Step-by-step explanation:

Given a quadratic equation

$2 {x}^{2} + 5x - 18 = 0$

To find the values of x.

Let's factorise the equation.

We shall follow the middle term splitting method.

So, we will get,

$= > 2 {x}^{2} + 9x - 4x - 18 = 0 \\ \\ = > 2 {x}^{2} - 4x + 9x - 18 = 0$

Taking the commom terms out, we get,

$= > 2x(x - 2) + 9(x - 2) = 0 \\ \\ = > (x - 2)(2x + 9) = 0$

Now, we have two cases.

CASE I

$= > x - 2 = 0 \\ \\ = > x = 2$

CASE II

$= > 2x + 9 = 0 \\ \\ = > 2x = - 9 \\ \\ = > x = - \dfrac{9}{2}$

Hence, the values of x = 2 and x = -9/2

Answer 2

$\bold\red{\underline{\underline{Answer:}}}$

$\bold\green{\underline{\underline{Solution:}}}$

$\bold{2x^{2}+5x-18=0}$

$\bold{2x^{2}+9x-4x-18=0}$

$\bold{x(2x+9)-2(2x+9)=0}$

$\bold{(2x+9)(x-2)=0}$

$\bold{(2x+9)=0 \ or \ (x-2)=0}$

$\bold{ x= \frac{-9}{2} \ or \ x=2}$