Question

Math factor and solve .

Answer 1

Answer:

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

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

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

$x=\frac{-1\pm\sqrt{(1)^2-4(3)(-2)}}{2(3)}$

which we simplify a bit to get

$x=\frac{-1\pm\sqrt{1+24}}{6}$$\Rightarrow x=\frac{-1\pm5}{6}$

which gives us two solutions:

$x=\frac{-1-5}{6}=-1$$x=\frac{-1+5}{6}=\frac{2}{3}$

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