Question

TIMED!!!!!The solutions to the equation 2x^2+x-1=2 are x=-3/2 or x=_____?

(The answer is 1)

Answer 1

1

Explanation:

Answer 2

ANSWER

`x = 1`


EXPLANATION

The equation is


`2 {x}^(2) + x - 1 = 2`


We group every term on the left hand side of the equation to obtain,




`2 {x}^(2) + x - 1 - 2 = 0`
This implies that,



`2 {x}^(2) + x - 3 = 0`

This is now a quadratic equation in

`x`
We multiply the coefficient of

`{x}^(2)`
which is 2, by the constant term which us

`- 3`
This gives

`- 6`

Two factors of -6 that adds up to 1 are

`3,-2`



We split the middle term with the factors,

`3,-2`


Thus, the equation becomes,



`2 {x}^(2) + 3x - 2x- 3 = 0`



We factor to obtain,



`x(2x + 3) - 1(2x - 3) = 0`


We factor further to obtain,


`(2x + 3)(x - 1) = 0`


This means that,


`x - 1 = 0 \: or \: 2x + 3 = 0`



`x = 1 \: or \: x = (3)/(2)`



Hence the other root is

`x = 1`