Question

3y^2-18y=-27Find the value of y.

Answer 1

`3y^2-18y=-27`

Before we can solve for the value of y, let's convert first the equation into a standard form ax² + bx + c = 0. Let's add 27 on both sides of the equation.

`3y^2-18y+27=-27+27`
`3y^2-18y+27=0`

Now, let's solve for the value of y.

Notice that the equation above is factorable by 3. Hence, the equation can also be written as:

`3(y^2-6y+9)=0`

Now, what we have to do is equate the quadratic equation in the parenthesis to zero and solve for y.

`y^2-6y+9=0`

Since the leading term is y² and its numerical coefficient is 1, we can find the factors of this equation by finding the factors of the constant term 9 that add up to the middle term -6.

Factors of 9

a. 3 and 3 → sum is 6

b. -3 and -3 → sum is -6

So, the factor of 9 that add up to -6 is just -3.

Hence, the equation can be factored into:

`(y-3)(y-3)=0`

Equate the factor to zero and solve for y.

`y-3=0`
`y-3+3=0+3`
`y=3`

Therefore, the value of y is 3.

Let's check if this is correct.

Replace the variable y in the original equation with 3.

`3(3)^2-18(3)=-27`

Then, simplify.

`3(9)-54=-27`
`27-54=-27`
`\begin{gathered} -27=-27 \\ TRUE \end{gathered}`

Indeed, by replacing the variable "y" with 3, both sides are equal to -27. Hence, the answer is correct.

ANSWER:

The value of y is 3.