Question

Use the quadratic formula to determine the exact solutions to the equation. x2−4x−8=0 Enter your answers in the boxes. x = or x =

Answer 1

Explanation:

Answer 2

The quadratic formula states that the solutions to the equation
`ax^2+bx+c=0` are (if they exist)

`x_(1,2) = (-b\pm√(b^2-4ac))/(2a)`

In your case, the quadratic equation is identified by the choice
`a = 1, b=-4, c=-8`, and this leads to the solutions

`x_(1,2) = (4\pm√(16+32))/(2) = (4\pm√(48))/(2)`

Since
`48 = 16\cdot 3`, we have

`√(48) = √(16\cdot 3) = √(16)\codt √(3) = 4√(3)`

So, the expression for the solutions becomes

`(4\pm4√(3))/(2) = 2\pm2√(3)`

So, the two solutions are
`2 + 2√(3)` and
`2 - 2√(3)`