56=a+a2

Rewrite the equation as a+a2=56.

a+a2=56

Move 56 to the left side of the equation by subtracting it from both sides.

a+a2-56=0

Let u=a. Substitute u for all occurrences of a.

u+u2-56

Factor u+u2-56 using the AC method.

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 -56 and whose sum is 1.

-7,8

Write the factored form using these integers.

(u-7)(u+8)

(u-7)(u+8)

Replace all occurrences of u with a.

(a-7)(a+8)

Replace the left side with the factored expression.

(a-7)(a+8)=0

(a-7)(a+8)=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-7=0

a+8=0

Set the first factor equal to 0.

a-7=0

Add 7 to both sides of the equation.

a=7

a=7

Set the next factor equal to 0.

a+8=0

Subtract 8 from both sides of the equation.

a=-8

a=-8

The final solution is all the values that make (a-7)(a+8)=0 true.

a=7,-8

Solve for a 56=a+a^2