x2+13x+42=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 42 and whose sum is 13.

6,7

Write the factored form using these integers.

(x+6)(x+7)=0

(x+6)(x+7)=0

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

x+6=0

x+7=0

Set the first factor equal to 0.

x+6=0

Subtract 6 from both sides of the equation.

x=-6

x=-6

Set the next factor equal to 0.

x+7=0

Subtract 7 from both sides of the equation.

x=-7

x=-7

The final solution is all the values that make (x+6)(x+7)=0 true.

x=-6,-7

Solve using the Square Root Property x^2+13x+42=0