Question

Solve by completing the square. x^2 + 7x-8 0

Answer 1

The equation x^2 + 7x - 80  =  0

Separate variables and constants aside by add 80 to each side.

x^2 + 7x - 80 + 80 =  0 + 80

x^2 + 7x  =  80

To change the expression into a perfect square trinomial add (half the x coefficient)² to each side of the expression.

x^2 + 7x + (7/2)^2   =  80 + (7/2)^2

x^2 + 7x + (7/2)^2   =  80 + (49/4)

(x + 7/2)^2   =  (320 + 49) / 4

(x + 7/2)^2   =  369 / 4

Take square root on both sides.

(x + 7/2)   =  √(369 / 4)

(x + 7/2)   =  √(9 X 41 / 4)

(x + 7/2)   =  3/2 √41

x   = - 7/2  ± 3/2 √41

Solutions are x   = - 7/2  + 3/2 √41 and x   = - 7/2  - 3/2 √41

Answer :

Solutions are x   = - 7/2  + 3/2 √41 and x   = - 7/2  - 3/2 √41