x: x2 - 81 = 0
x3=x2 x3-x2=0 Factor out x2 x2(x - 1) = 0 If x2=0 then x=0. If x - 1 = 0 then x = 1. Therefore the number is 0 or 1.
x=8
x2 - 7x = 60 x2 - 7x - 60 = 0 (x - 12) (x + 5) = 0 x = 12 or x = -5
x2 = 8xx2- 8x = 0x(x - 8) = 0x = 0 ;x - 8 = 0x = 8
x2 23x equals 0
(23/2)2 x2 - 23x = 0 x2 - 23x + (23/2)2 = (23/2)2 (x - 23/2)2 = (23/2)2 x - 23/2 = 23/2 x = 23/2 + 23/2 x = 23 Of course you could come to this solution much more easily by dividing the whole equation by x at the start. There really is no need to complete the square in this case: x2 - 23x = 0 x - 23 = 0 x = 23
The discriminant is 25.
x: x2 - 81 = 0
If: x2-4 = 0 Then: x = 2
X + Y = 23 XY = 132 Y = 23-x xy = x (23-x) = 23x -x2= 132 x2-23x+132 = 0 (X-11)(x-12) = 0 X = 11 Y = 12
x2 + 49 = 0 ∴ x2 = -49 ∴ x = 7i
x2 + 7x = 2x2 + 6 x2 - 2x2 + 7x = 6 -x2 +7x - 6 = 0 or alternatively x2 - 7x + 6 = 0
144X = X2 144X - X2 = 0 (144 - X)X = 0 X = 0 or X = 144
x2-10 = 0 x2 = 10 x = the square root of 10
x = 0
The domain of y = x2 is [0,+infinity]