How do I solve this equation? 5x^2 = -8x

To solve 5x^2 = -8x.

Solution:

Method (1):

5x^2= -8x . Dividing bot sides by x, we get:

5x=-8 or x= -8/5 = - 1.6.

Also 5x^2+8x = 0 has noconstant term . So x =0 is root of it.

Method 2:

5x^2+8x = 0 This is a quadratic equation of the form ax^2+bx+c = 0, Where, a=5, b= 8 and c= 0. Therefore,the roots are:

x1 =(-b+(b^2-4ac)^0.5)/(2a)  and

x2 = (-b-(b^2-4ac)^0.5)/(2a).

X1 = (-8+(8^2-4*8*0)^0.5)/(2*5) = 0

X2 = (-8-(8^2-4*8*0)^0.5)/(2*5) =-16/10 =-1.6

Method (3):

5x^2 =-8x  or

5x^2+8x = 0. We can write this like,

5(x^2+1.6x+0.8^2)^2 - 5*0.8^2 = 0 or

5(x+0.8)^2 = 5*0.8^2. Dividing both sides by 5,

(x+0.8)^2 = 0.8^2 . Taking square root, we get:

x+0.8 = +0.8 ............(1) or

x+0.8 =-0.8..............(2)

From(1) we get: x= 0

From (2) we get: x =  -0.8-0.8 = -1.6