perfect square equation

Question

x² + 12x -64 =0

Transform each equation into a perfect square equation and solve.

Answer 1

The perfect square equation is x2 + 12x- 64 = 0.
Add 36 each side. x2 + 12x -64 + 36 = 0 + 36 x2 + 12x + 36 - 64 = 36 Add 64 each side. x2 + 12x + 36 - 64 + 64 = 36 + 64 x2 + 12x + 36 = 100 The above equation we can write it as follows (x + 6)2 = 100 x+6 =√100 x + 6 = ± 10 x+6=10 or x+6=-10 x+6=10 subtract 6 from each side. x+6-6=10-6 x = 4 x+6=-10 subtract 6 from each side. x+6-6=-10-6 x=-16 The solution set of x={4,-16}.

 

Answer 2

x² + 12x - 64 = 0

Separate variables and constants aside by adding 64 to each side.

x² + 12x = 64

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

 Here x coefficient = 12. so, (half the x coefficient)² = (12/2)²= 36

Add 36 to each side

x² + 12x + 36 = 64 + 36

(x + 6)²= 100

Take square root both sides

x + 6 = ±√10

x = -6 ± 10

x = -16, 4