In all cases, it is not convenient to solve a quadratic equation by factorization method. Thus, to solve the given quadratic equation, we use an alternative method, called completing the square method. In this sub-topic, we will learn a method for solving any kind of quadratic equation.

If x² + 8x is the beginning of a perfect square expression, what should be the constant term?

Let us assume that the expression can be factored as the perfect square (x + k)² where the value of constant k is still unknown. This expression is expanded as x² + 2kx + k², which tells us two things:

1. The coefficient of x, which we know to be 8, should be equal to 2k. This means that k = 4.
2. The constant number we need to add is equal to k², which is 42 = 16.

In general, to solve a quadratic equation using completing the square method, we follow the following steps.

Step 1: Write the given quadratic equation in the standard form.
Step 2: Make the coefficient of x² equal to 1, if it is not.
Step 3: Shift the constant term to right hand side (R.H.S) of the equation.
Step 4: Express the left-hand side (L.H.S) as the perfect square of a suitable binomial expression and simplify the right-hand side (R.H.S).
Step 5: Take square root of both sides.
Step 6: Obtain the values of x by shifting the constant term from L.H.S to R.H.S.