Can anyone teach me how to solve a Quadratic equation by completing the square? Thanks..
The idea behind completing the square is to add or subtract a constant to obtain the form
Step 1: Divide both sides by
Step 2: Add
Step 3: Add a constant to both sides which will allow us to factor the left hand side as
Step 4: Factor the left hand side
Step 5: Take the square root of both sides. Remember to account for both positive and negative roots.
Step 6: Solve the remaining linear equation:
The real trick here is observing in step 3 that the constant we need to add is equal to the square of half of the coefficient of
Let's see what happens if we apply this to a general quadratic equation.
And we have just derived the quadratic formula.