n2+20n+75=0

Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is 75 and whose sum is 20.

5,15

Write the factored form using these integers.

(n+5)(n+15)=0

(n+5)(n+15)=0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

n+5=0

n+15=0

Set the first factor equal to 0.

n+5=0

Subtract 5 from both sides of the equation.

n=-5

n=-5

Set the next factor equal to 0.

n+15=0

Subtract 15 from both sides of the equation.

n=-15

n=-15

The final solution is all the values that make (n+5)(n+15)=0 true.

n=-5,-15

Solve using the Square Root Property n^2+20n+75=0