Question

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

Answer 1

Answer:

-2 +or- √7 / 3

Step-by-step 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 $x=\frac{-b+/-\sqrt{b^2-4ac}}{2a}$ , with a = x^2 coefficient, b = x coefficient, and c = constant. Our equation will look like this: $x=\frac{-4+/-\sqrt{4^2-4*3*(-1)}}{2*3}$

Firstly, solve the exponents and multiplications: $x=\frac{-4+/-\sqrt{16+12}}{6}$

Next, do the addition, and your exact solutions are: $x=\frac{-4+\sqrt{28}}{6}$ and $x=\frac{-4-\sqrt{28}}{6}$