Algebra 1 problem

Question

Solve completly. Please show work: 18y^2 + 8 = 24y

Answer 1

18y²+8=24y

18y²-24y+8=0

divide both sides by 2

9y²-12y+4=0

9*4=36=6*6 and 6+6=12

this is a square trinomial

(3y-2)(3y-2)=0

3y-2=0

3y=2

y=2/3

this is a double root

Answer 2

Sophie,

 

Let's rearrange the equation to get:

 

18y² -24y +8 = 0

 

To make factoring the quadratic easier, let's factor out 2 from the expression.

 

2(9y² - 12y + 4) = 0

 

Next, we need to factor the quadratic expression.  Since we have a negative b term (-12) and positive c term (+4), this means that we have to have factor expressions in the form (dx - e)(fx-g).  Factoring, we get:

 

2(3y-2)(3y-2) = 0

 

(3y-2)(3y-2) = 0

 

Or

 

3y-2 = 0

 

3y=2

 

So y = 2/3  which is a double root.

 

Hope this helps!