Question

Use the given function to find the indicated value(s) of x. (Enter your answers as a comma-separated list.)

For f(x) = √2x + 2 − √x + 18, find x such that f(x) = −1.

Answer 1

For f(x) = √(2·x + 2) - √(x + 18), at f(x) = -1 the possible x-values includes;

-0.757, -17.5

Explanation:

Given that the function is f(x) = √(2·x + 2) - √(x + 18)

The value of 'x' when f(x) = -1, is given as follows;

-1 = √(2·x + 2) - √(x + 18)

-1² = (√(2·x + 2) - √(x + 18))² = 3·x + 20 - 2·√(2·x + 2)×√(x + 18)

1 = 3·x + 20 - 2·√(2·x + 2)×√(x + 18)

2·√(2·x + 2)×√(x + 18) = 3·x + 20 - 1 = 3·x + 19

2·x² + 38·x + 36 = (3·x + 19)/2

2·x² + 38·x + 36 - (3·x + 19)/2 = 0

4·x² + 73·x + 53 = 0

From which we get;

x = (-73 ± √(73² - 4 × 4 × 53))/(2 × 4)

x ≈ -0.757, and x ≈ -17.5