Question

Use algebra to solve 3x + 4 =1/x . The exact solutions are x =

Answer 1

-2 +or- √7 / 3

Explanation:

The exact answer is x = -4 - √28 / 6 but has to be solved with the quadratic formula giving you -2 + or - √7 / 3

Answer 2

So firstly, you want to multiply x on each side of the equation:
`3x^2+4x=1`

Next, subtract 1 on each side:
`3x^2+4x-1=0`

Next, we will be using the quadratic formula, which is
`x=(-b+/-√(b^2-4ac))/(2a)` , with a = x^2 coefficient, b = x coefficient, and c = constant. Our equation will look like this:
`x=(-4+/-√(4^2-4*3*(-1)))/(2*3)`

Firstly, solve the exponents and multiplications:
`x=(-4+/-√(16+12))/(6)`

Next, do the addition, and your exact solutions are:
`x=(-4+√(28))/(6)` and
`x=(-4-√(28))/(6)`