Question

Solve 9x^2 + 42x + 49 = 0

Answer 1

Because of the relatively large coefficients {9, 42, 49}, applying the quadratic formula would be a bit messy. Instead, I've chosen to "complete the square:"

9x^2 + 42x + 49 = 0 can be re-written as 9 [ x^2 + (42/9)x ] = -49

Dividing both sides by 9, we get [ x^2 + (42/9)x ] = - 49/9

Completing the square: [ x^2 + (42/9)x + (21/9)^2 - (21/9)^2 ] = -49/9

[ x + 21/9 ]^2 = 441/81 - 441/81 = 0

Then [ x + 21/9 ] = 0, and x = -21/9 (this is a double root).