What must be added to X2+10x+23to make it perfect square
well, 10/2 = 5
(x+5)^2 = ?
To make the expression X^2 + 10x + 23 a perfect square, we need to add a certain term in order to form a perfect square trinomial.
To do this, we can follow these steps:
1. Identify the first two terms: In our case, the first two terms are X^2 + 10x.
2. Take half of the coefficient of the middle term and square it: The middle term in our case is 10x. Half of 10x is 5x, and squaring it gives us 25x^2.
3. Add the squared term to both sides of the expression: Adding 25x^2 to both sides of the equation X^2 + 10x + 23 = 0 gives us X^2 + 10x + 25x^2 + 23 = 25x^2.
4. Simplify the trinomial: Combining like terms, we get X^2 + 10x + 25x^2 + 23 = 26x^2 + 10x + 23.
So, to make X^2 + 10x + 23 a perfect square, we need to add 25x^2 to it. The resulting expression will be 26x^2 + 10x + 23, which is a perfect square.