Which of the following is a value of x that satisfies the equation `x ^(2) + 2x -5 =0` ?

Options

A. `-1`
B. `1- sqrt6`
C. `1 + sqrt6`
D. `-1-sqrt6`

Answer

D

Explanation

Factoring won't work here because no two factors of -5 sum to 2. However, the coefficient of `x ^(2)` is 1, so try completing the square:
`x ^(2) + 2x -5 =0`
`x ^(2) + 2x =5`
`((b)/(2))^(2)= ((2)/(2))^(2) =1 ^(2) =1`
`x ^(2) + 2x +1 =5 +1`
`(x+1)^(2) =6`
` x +1 =pm sqrt6`
x =- 1 pm sqrt6`
(D) matcvhes one of the two possible values of x, so it's correct.