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

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Assuming you've typed this in correctly, here's how you do this.

First, you need to try to get one side to not have an x anymore -- get all the x terms on one side. To do this, you can divide both sides by x.

If you do that, you get

5x = -8

From there, all you do is divide by 5. That gets you

x = -8/5 or x = -1.6

If you wanted to, you could do this in just one step. You could just divide both sides by 5x right away and still get the same answer.

`5x ^ 2 = -8x`

`5x^2 + 8x=0`

`x( 5x + 8)=0`

x=0

5x + 8 = 0

`-8/5`

5x ^ 2 = -8x

5x^2 + 8x=0

x ( 5x + 8)=0

x=0

5x + 8 = 0

-8/5

5x^2 = -8x

move them to the same side

5x^2 + 8x

now they have a common factor of x so factor it out

x (5x + 8)

now set them equal to 0

x = 0

5x + 8 = 0

subtract 8

5x = -8

divide by 5

x = -8/5

`5x^2 = -8x`

You might be tempted to divide by x as a means of simplifying the problem. But its recommended you don't since you'll divide out a solution. (In this case, you'd divide out the solution that x = 0 )

To avoid complications, just get all your variable terms on one side of the equation:

`5x^2 + 8x = 0`

*factor*out the x.

5x^2=-8x

Then move everything to one side

5x^2+8x=0

Separate the variable

x(5x+8)=0

then

x=0

5x=-8 ----> x=-8/5

5x^2 = -8x

5x^2+8x=0

x(5x+8)=0

so

x=0 or (-8/5)

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

The given equation is:

5x^2 = -8X

We rewrite the equation by shifting the term on right hand side on left hand side:

5x^2 + 8x = 0

Therefor:

x*(5x + 8) = 0

Or: 5*x*(x + 8/5) = 0

Therefor there are two possible values of x: x= 0 and x = -8/5 = -1.6