(a + b)^2.

So if your question is not asking you to solve for x, and your question is simply asking you to “complete the square,” then this is all you have to do:

(x^2 + 10x)

Take the second term, half it, and then square it:

(10 / 2)^2 = 5^2 = 25

Now, add this number to the above expression, and subtract it to “balance” the expression:

(x^2 + 10x) + 25 – 25 = (x^2 + 10x + 25) – 25

Now notice how (x^2 + 10x + 25) = (x + 5)^2, so your expression becomes:

(x + 5)^2 – 25.

Done. “The square is completed” because I just turned a quadratic, (x^2 + 10x + 25), into a perfect square trinomial,

(x + 5)^2. This is all you have to do to “complete the square.” No need for radicals and any more work.

take the second term, halve it and then square it

(10/2 = 5, 5^2 = 25)

plug it in like so, so that the expression remains the same if simplified

(x^2 + 10x + 25) – 25

factorize the expression in the brackets and the term outside (difference of perfect squares)

(x + 5)^2 – (√25)^2

The following uses the rule a^2 – b^2 = (a + b)(a – b)

= (x + 5 + √25)(x + 5 – √25)

= (x + 5 + 5)(x + 5 – 5)

= x(x + 10)

This is not a good example of completing the square, as the common factor of x can simply be taken out of the equation to factorise it.

Completing the square is used when you cannot factorise an equation by taking out a common factor, using the cross method, or using difference of perfect squares.

A better example would be:

x^2 + 6x + 2

= (x^2 + 6x + 9) + 2 – 9

= (x + 3)^2 – (√7)^2

= (x + 3 + √7)(x + 3 – √7)

= (x^2 + 10x) (x^2 + 10x)

= x^4 + 10x^3 + 10x^3 + 100x^2

= x^4 + 20x^3 + 100x^2 –> Answer.

PS- Formula is – (a+b)^2 = a^2 + 2 ab + b^2