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

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pohnpei397's profile pic

pohnpei397 | College Teacher | (Level 3) Distinguished Educator

Posted on

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.

 

fashionableb1's profile pic

fashionableb1 | Student, Grade 10 | (Level 1) Salutatorian

Posted on

5x ^ 2 = -8x

5x^2 + 8x=0

x ( 5x + 8)=0

x=0

5x + 8 = 0

-8/5

 
 
atyourservice's profile pic

atyourservice | Student, Grade 11 | (Level 3) Valedictorian

Posted on

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

Wiggin42's profile pic

Wiggin42 | Student, Undergraduate | (Level 2) Valedictorian

Posted on

`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`

 Now factor out the x. 
 
x ( 5x + 8) = 0
 
We have to factors being multiplied together that end up being equal to zero. Therefore one of these factors need to equal zero. 
5x + 8 = 0                 and                  x = 0

Solve for x: 
x = -8/5       and           x = 0
zumba96's profile pic

zumba96 | Student, Grade 11 | (Level 3) Valedictorian

Posted on

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

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

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

 

krishna-agrawala's profile pic

krishna-agrawala | College Teacher | (Level 3) Valedictorian

Posted on

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

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