Question

Find the
value of x
2x²+x-4=0​

Answer 1

Answer:

First we will use split the middle term method -

for that we will first divide the equation by 1/2,

The the equation will be,

= x² + x/2 - 4

By multiplying and dividing the middle term by 2 to get 2ab as we need get it as ,

(a² + b²) = a² + 2ab + b²

= x² + 2 × (1/4)x - 2 = 0

=> By adding (1/4)² both the sides ,

we get,

=> x² + 2(1/4)x + (1/4)² - 2 = (1/4)²

It can be, reduced to the form (a + b)²

=> ( x + 1/4 )² - 2 = 1/16

=>  (x + 1/4)² = 1/16 + 2

=> (x + 1/16)² = (1 + 32)/16

=> (x+ 1/16)² = 33 / 16

By moving the square from LHS to RHS, we get,

=> x+ 1/4 = 33/16 route 2

 

=> x + 1/4 = (33 route 2) / 4   (or) x + 1/4 = (33 route 2) / 4

=>  x = [ ( 33 route 2 )] - 1 / 4

HENCE ITS COMPLETE.

I HOPE ITS HELPFUL.