## Algebra

This is the derivation of an equation we all know. The equation:

(1)

As a solution to this:

(2)

STEP 1, set the coefficient of the first term to one.

(3)

STEP 2, Subtract the third term from both sides:

(4)

STEP 3, Take one half of the middle term, square it and add to both sides of the equation:

(5)

The goal here is to get the left hand term to be a perfect square trinomial. STEP 4. Factor the left hand side of the equation.

(6)

Step 5, Find the least common denominator for the right hand side:

(7)

STEP 6, Take the square root of both sides:

(8)

Step 7, Solve for x

(9)