Question

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

Answer 1

Answer:

1

Step-by-step 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,

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


$x = 1 \: or \: x = \frac{3}{2}$



Hence the other root is
$x = 1$