Problem 7 - Algebra 1

Question

Find the term that should be added to the expression to create a perfect square trinomial. $$x^{2}-22 x$$

Step-by-Step Solution

Answer

The term that should be added to the expression to create a perfect trinomial is 121.

Step 1: Identify the Coefficient in Given Binomial

First, observe the given expression \(x^{2} - 22x\). The coefficient of \(x\), which is analogous to \(2ab\) in the formula, is -22.

Step 2: Calculate b

Next, we calculate the value for \(b\) which gives the missing term in the perfect square. The formula for finding \(b\) is derived from the equation \(2ab = -22\), where \(a\) is 1 (since the coefficient of \(x^{2}\) is 1), so \(b = -22/(2 * 1) = -11\)

Step 3: Compute the Square of b

Lastly, we find \(b^{2}\) which is the term to be added. So, \((-11)^{2} = 121\). Thus, the term that should be added to the expression to create a perfect trinomial is 121.