Quadratic Equations solve by factoring y^2+8y=0 Does anyone know how to solve this??

Question

Quadratic Equations solve by factoring y^2+8y=0 Does anyone know how to solve this??

Answer 1

Question Number 1 :

For this equation y^2 + 8*y  = 0 , answer the following questions :

A. Find the roots using Quadratic Formula !

B. Use factorization to find the root of the equation !

C. Use completing the square to find the root of the equation !

Answer Number 1 :

The equation y^2 + 8*y  = 0 is already in a*x^2+b*x+c=0 form.

As the value is already arranged in a*x^2+b*x+c=0 form, we get the value of a = 1, b = 8, c = 0.

1A. Find the roots using Quadratic Formula !

  Remember the formula,

    y1 = (-b+sqrt(b^2-4*a*c))/(2*a) and y2 = (-b-sqrt(b^2-4*a*c))/(2*a)

  Since a = 1, b = 8 and c = 0,

  we just need to subtitute the value of a,b and c in the abc formula.

  Which produce y1 = (-(8) + sqrt( (8)^2 - 4 * (1)*(0)))/(2*1) and y2 = (-(8) - sqrt( (8)^2 - 4 * (1)*(0)))/(2*1)

  Which make y1 = ( -8 + sqrt( 64+0))/(2) and y2 = ( -8 - sqrt( 64+0))/(2)

  Which is the same as y1 = ( -8 + sqrt( 64))/(2) and y2 = ( -8 - sqrt( 64))/(2)

  So we get y1 = ( -8 + 8 )/(2) and y2 = ( -8 - 8 )/(2)

  So we got the answers as y1 = 0 and y2 = -8

1B. Use factorization to find the root of the equation !

  y^2 + 8*y  = 0

  ( y  ) * ( y + 8 ) = 0

  The answers are y1 = 0 and y2 = -8

1C. Use completing the square to find the root of the equation !

  y^2 + 8*y  = 0 ,divide both side with 1

  By doing so we get y^2 + 8*y  = 0 ,

  The coefficient of y is 8

  We have to use the fact that ( y + q )^2 = y^2 + 2*q*y + q^2 , and assume that q = 8/2 = 4

  Which means we can turn the equation into y^2 + 8*y + 16 - 16 = 0

  Which can be turned into ( y + 4 )^2  - 16 = 0

  And it is the same with (( y + 4 ) - 4 ) * (( y + 4 ) + 4 ) = 0

  By opening the brackets we will get ( y + 4 - 4 ) * ( y + 4 + 4 ) = 0

  Do the addition/subtraction, and we get ( y  ) * ( y + 8 ) = 0

  So we got the answers as y1 = 0 and y2 = -8

Answer 2

y^2 + 8y=0

y(y + 8 ) = 0  - Giving y  = 0

y + 8 = 0

Therefore y = - 8  or y =0

Answer 3

y(y + 8) = 0

Therefore y = 0 or y + 8 = 0

So.... y = 0 or y = -8  (ANSWER)

Take care,

David

Answer 4

first factor out the y:

y² +8y =0

y(y+8) = 0

so either y =0 or y+8 =0

meaning y=0 or -8

Answer 5

            y^2 + 8y = 0

=>      y (y+8)=0

=>       y=0 or y+8=0

=>       y=0 or y= -8  

Answer 6

y^2 + 8y = 0

This is fairly simple, all you need to do is factor and use the zero product property.

What is the common factor in this equation? y.

y(y+ 8) = 0 Factored.

y = 0

or

y + 8 = 0

y = -8

Now you have two solutions. Substitute them into the original equation and check for any extranous solutions. Your final answer should be y = -8 and y = 0

Answer 7

Upon looking carefully, you should see that y is a common denominator of both y^2 and 8y.  Therefore your problem can be rewritten as:

(y)(y+8) = 0

y = 0 is your first answer

y + 8 = 0

y = -8 is your second answer

Final Answer:   y = 0   and y = -8

Answer 8

y (y + 8) = 0

y = 0 , y = - 8

Answer 9

y^2 + 8y = 0

take out y common so u get

y(y + 8) = 0

so u get two solutions for the equation

y = 0  and y= -8