a2+7a+10=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 10 and whose sum is 7.

2,5

Write the factored form using these integers.

(a+2)(a+5)=0

(a+2)(a+5)=0

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

a+2=0

a+5=0

Set the first factor equal to 0.

a+2=0

Subtract 2 from both sides of the equation.

a=-2

a=-2

Set the next factor equal to 0.

a+5=0

Subtract 5 from both sides of the equation.

a=-5

a=-5

The final solution is all the values that make (a+2)(a+5)=0 true.

a=-2,-5

Solve for a a^2+7a+10=0