Question

Use the quadratic formula to determine the exact solutions to the equation x^2-4x-8=0

Answer 1

The answer is 2+2√3 or 2-2√3

Answer 2

`x = 2`±
`√(12)`

Explanation:

Given the following equation ax^2 + bx + c = 0, the quadratic formula states that the solution to that equation is going to be given by:

`x1 = \frac{-b+\sqrt{b^(2)-4ac } }{2a}`

`x1 = \frac{-b-\sqrt{b^(2)-4ac } }{2a}`

In this case, a=1, b=-4 and c=-8. Therefore:

`x1 = \frac{4+\sqrt{(-4)^(2)-4(1)(-8)} }{2}`

`x1 = (4+√(48))/(2)`

`x1 = 2+√(12)`

`x2 = \frac{4-\sqrt{(-4)^(2)-4(1)(-8)} }{2}`

`x2 = (4-√(48))/(2)`

`x2 = 2-√(12)`

Therefore the solutions are:

`x = 2`±
`√(12)`