Question

Math factor and solve .

Answer 1

x = -1 and x = 2/3

Explanation:

The equation given is a quadratic equation.

Therefore, to solve for x we use the quadratic formula.

The quadratic formula says that if we have an equation of the form

`ax^2+bx+c=0`

Then the values of x (solutions) are given by

`x=(-b\pm√(b^2-4ac))/(2a)`

Now in our case, the equation we have is

`3x^2+x-2=0`

which tells us that a = 3, b = 1, and c = -2; therefore, quadratic formula gives

`x=(-1\pm√((1)^2-4(3)(-2)))/(2(3))`

which we simplify a bit to get

`x=(-1\pm√(1+24))/(6)`
`\Rightarrow x=(-1\pm5)/(6)`

which gives us two solutions:

`x=(-1-5)/(6)=-1`
`x=(-1+5)/(6)=(2)/(3)`

Hence, the two solutions to the quadratic equation are x = -1 and x = 2/3.