(9y-3)(y-1)=-2

Question

solve and write an equation set 

Answer 1

Hi Karen.

 

To write an equation set for (9y-3)(y-1) = -2, we will use FOIL to multiply these 2 binomials and then combine like terms to get our quadratic equation for this solution set:

 

<F>irst     <O>utside    <I>nner     <L>ast  

(9y)(y)  + (9y)(-1)      + (-3)(y)    + (-3)(-1)   = -2

 

9y² - 9y -3y =3 = -2

 

Combining like terms and setting right side to zero:

 

9y² - 12y - 5 = 0 (our quadratic equation)

 

Now let's factor the left side:

 

First we multiply the coefficient of y² term (9) by the constant term (-5) to get -45.

 

Next, we look for two factors of -45 which will add up to coeffiecient of middle term (-12) and get our factors of -15 and 3.

 

Next, we rewrite equation to express coefficient of middle term as sum of these two factors:

 

9y² + (-15 + 3)y - 5 = 0

 

Next, we rewrite equation by distributing (multiplying) these two factors with y:

 

9y² - 15y + 3y - 5 = 0

 

(9y² + 3y) - (15y + 5) = 0 (regroup four terms into two easily factorable binomial pairs)

 

3y(3y + 1) - 5(3y + 1) = 0 (factor each binomial pair)

 

(3y + 1)(3y - 5) = 0 (pull out common factor of
3y + 1 from each factored binomial pair)

 

Setting each factor to zero and solving each equation for y we get our two solutions:

 

3y + 1 = 0; y = -1/3

3y -5 = 0; y = 5/3

 

Trust the above step-by-step explanation will be helpful to your understanding of this problem's solution.

 

Regards, Jordan.