What value should be added to the expression x² + 10x to make it a perfect square trinomial?

by

To convert the expression x² + 10x into a perfect square trinomial, we need to find a specific value that, when added, completes the square.

A perfect square trinomial takes the form (x + a)², which expands to x² + 2ax + a². In this case, we have:

  • The coefficient of x is 10
  • In the expanded form, 2a must equal 10

To find a, we set up the equation:

2a = 10

Dividing both sides by 2 gives:

a = 5

Now, to complete the square, we square a:

a² = 5² = 25

This means we need to add 25 to the original expression:

x² + 10x + 25

Thus, the expression x² + 10x + 25 can be factored into:

(x + 5)²

In conclusion, by adding 25 to the expression x² + 10x, we create a perfect square trinomial, allowing for easier factoring and solving of related quadratic equations.

Leave a Comment