Completing the Square Formula

In elementary algebra, completing the square is a technique for converting a quadratic polynomial to a perfect square added to some constant. This method is used for solving the quadratic equation.

In mathematics, completing the square is often applied in any computation involving quadratic polynomials. Completing the square is also used to derive the quadratic formula.

Completing the Square Formula is given as

$a x^{2} + b x + c \Rightarrow (x + p)^{2} + c o n s t a n t$

Solved Examples

Question 1: Solve
$\begin{array}{l} x^{2} \end{array}$
+ 6x -2 = 0
Solution:

\begin{array}{l} x^{2} \end{array}

+ 6x – 2 = 0 can be written as

\begin{array}{l} (x + 3)^{2} \end{array}

– 11 = 0

So, to solve the equation, take the square root of both sides. So

\begin{array}{l} (x + 3)^{2} \end{array}

= 11

x+3=+

\begin{array}{l} \sqrt{11} \end{array}

or x+3=-

\begin{array}{l} \sqrt{11} \end{array}

x= -3+

\begin{array}{l} \sqrt{11} \end{array}

or x= -3 -

\begin{array}{l} \sqrt{11} \end{array}

\begin{array}{l} \sqrt{11} \end{array}

=3.317

x = -3 +3.317 or x = -3 -3.317,

x=0.317 or x= -6.317

Completing the Square Formula

Solved Examples

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