Question

solve the equation by completing the square. x^2 -6x -21=0 if the solution is not a real number enter no solution (ANSWER -2.48 and 8.48 )this is what the lesson says i just dont know how to show this

Answer 1

see explanation

Explanation:

given x² - 6x - 21 = 0 ( add 21 to both sides )

x² - 6x = 21

to complete the square

• add ( half the coefficient of the x-term)² to both sides

x² + 2 (- 3)x +9 = 21 + 9

(x - 3)² = 30 ( take the square root of both sides )

x - 3 = ±
`√(30)` ( add 3 to both sides )

x = 3 ±
`√(30)`

x = 3 -
`√(30)` = - 2.48 ( to 2 dec. places ) or

x = 3 +
`√(30)` = 8.48 ( to 2 dec. places )