Question

How do you solve `6x² + x = 2`?

Answer 1

The solutions are:

`color(blue)(x= 1/2`

`color(blue)(x= -2/3`

Explanation:

`6x^2 + x = 2`

`6x^2 + x - 2 =0`

The equation is of the form `color(blue)(ax^2+bx+c=0` where:

`a=6, b=1, c= - 2`

The Discriminant is given by:

`Delta=b^2-4*a*c`

`= (1)^2-(4* 6 * (-2))`

`= 1 + 48 = 49`

The solutions are found using the formula
`x=(-b+-sqrtDelta)/(2*a)`

`x = ((-1)+-sqrt(49))/(2*6) = (-1+-7)/12`

`x= (-1+7)/12 = 6/12 = 1/2`

`x= (-1-7)/12 = -8/12 = -2/3`

Answer 2

The method of finding the solution will depend on the grade in which it is being dealt with. An alternative method is to factorise.
`x= 1/2` or `x = -2/3`

Explanation:

To solve a quadratic `(x^2)` equation, always make it equal to 0.

In simple algebra there are then three methods available to find the solution: factorise, complete the square or the quadratic formula.

`6x^2 + x - 2 = 0` factorises into `(2x-1)(3x+2) = 0`

The fact that a product of two factors results in 0 means that at least one of the factors must be equal to 0.

If `2x-1 = 0,` then `2x = 1 and x = 1/2`

If `3x+2 = 0,` then `3x = -2 and x = -2/3`