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

ANSWER
[tex]x = 1[/tex]


EXPLANATION

The equation is

[tex]2 {x}^{2} + x - 1 = 2[/tex]


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



[tex]2 {x}^{2} + x - 1 - 2 = 0[/tex]
This implies that,


[tex]2 {x}^{2} + x - 3 = 0[/tex]

This is now a quadratic equation in
[tex]x[/tex]
We multiply the coefficient of
[tex] {x}^{2} [/tex]
which is 2, by the constant term which us
[tex] - 3[/tex]
This gives
[tex] - 6[/tex]

Two factors of -6 that adds up to 1 are
[tex]3,-2[/tex]



We split the middle term with the factors,
[tex]3,-2[/tex]


Thus, the equation becomes,


[tex]2 {x}^{2} + 3x - 2x- 3 = 0[/tex]



We factor to obtain,


[tex]x(2x + 3) - 1(2x - 3) = 0[/tex]


We factor further to obtain,

[tex](2x + 3)(x - 1) = 0[/tex]


This means that,

[tex]x - 1 = 0 \: or \: 2x + 3 = 0[/tex]


[tex]x = 1 \: or \: x = \frac{3}{2} [/tex]



Hence the other root is
[tex]x = 1[/tex]