4+b2=5b

Subtract 5b from both sides of the equation.

4+b2-5b=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 4 and whose sum is -5.

-4,-1

Write the factored form using these integers.

(b-4)(b-1)=0

(b-4)(b-1)=0

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

b-4=0

b-1=0

Set the first factor equal to 0.

b-4=0

Add 4 to both sides of the equation.

b=4

b=4

Set the next factor equal to 0.

b-1=0

Add 1 to both sides of the equation.

b=1

b=1

The final solution is all the values that make (b-4)(b-1)=0 true.

b=4,1

Solve for b 4+b^2=5b