Question

Solve the quadratic equation by completing the square 4x^2+8x-7=0

help please.

Answer 1

The given equation is:
`4x^(2)`+8x-7=0
We will solve using completing the square:
On dividing both the sides by 4 , we get,


`x^(2) + (8x)/(4) - (7)/(4)` =0
Now, adding 1 to both sides we get,


`x^(2) + (8x)/(4) - (7)/(4)` + 1 = 1

On rearranging the terms we get,


`(x^(2) + 2x + 1) = 1 + (7)/(4)`

`(x + 1)^(2)` = 1 +
`(7)/(4)`


`(x+1 )^(2) = (11)/(4)`

On taking sqaure root we get,

`(x + 1) = + ( √(11) )/(2) ; - ( √(11) )/(2)`

Therefore,
`image`
`x = - ( √(11) )/(2) -1`