Question

Given the function y = x2 + 2x - 8, what are the values of x when y = 3?

Answer 1

`x = - 1 + 2 √(3)`

`x = - 1 - 2 √(3)`

Explanation:

`{x}^(2) + 2x - 8= 3`

`{x}^(2) + 2x = 11`

Complete the square

`((2)/(2) ) {}^(2) = 1`

so

`{x}^(2) + 2x + 1 = 11 + 1`

`{x}^(2) + 2x + 1 = 12`

`( x + 1) {}^(2) = 12`

`x + 1 = √(12)`

`x = - 1 + √(12)`

or

`x + 1 = - √(12)`

`x = - 1 - √(12)`

If you want it simplified, you could say