Question

Solve the following quadratic equation by factoring. if needed, write your answer as a fraction we just do those terms.

Answer 1

y= -10 or 4

Step-by-step explanation

given

`y^2+6y=40`

Step 1

factor

a)subtrac 40 in both sides

`\begin{gathered} y^2+6y=40 \\ y^2+6y-40=40-40 \\ y^2+6y-40=0 \end{gathered}`

b)write 6y as 10y -4y

so

`\begin{gathered} y^(2)+6y-40=0 \\ y^2+10y-4y-40=0 \end{gathered}`

c) group and facrtor the common term

`\begin{gathered} y^(2)+10y-4y-40=0 \\ y(y+10)-4(y+10)=0 \\ (y+10)\text{ is the common factor, so} \\ (y+10)(y-4)=0 \end{gathered}`

so, the new expression is

`(y+10)(y-4)=0`

Step 2

solve for x

`(y+10)(y-4)=0`

when the product of 2 factors equals zero, it means one or both factors equals zero, so

`\begin{gathered} (y+10)(y-4)=0 \\ (y+10)=0 \\ solve\text{ for y, subtract 10 in both sides} \\ (y+10)-10=0-10 \\ y=-10\Rightarrow solution \\ \end{gathered}`

and

`\begin{gathered} (y+10)(y-4)=0 \\ (y-4)=0 \\ solve\text{ for y, add 4 in both sides} \\ (y-4)+4=0+4 \\ y=4\Rightarrow solution \\ \end{gathered}`

so, the answer is

y= -10 or 4

I hope this helps you