# Solve for a 56=a+a^2 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
Factor the left side of the equation.
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 and solve.
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 and solve.
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

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