Question

Solve the equation x^2 + 5x = -1 by completing the square.

Answer 1

The answer to your question is: the third option

Explanation:

x² + 5x = - 1

x² + 5x +
`((5)/(2)) ^(2)` = -1 +
`((5)/(2) )^(2)`

(x +
`(5)/(2)`)² = - 1 + 25/4

(x +
`(5)/(2)`)² = (-4 + 25) / 4

(x +
`(5)/(2)`)² = 21/4

(x +
`(5)/(2)`) = ±
`\sqrt{(21)/(4) }`

x =
`(5)/(2) ±   (√(21))/(2)`

x =
`(-5 ± √(21) )/(2)`