Question

What term should be added to create a perfect square trinomial?x2 + 22x

Answer 1

Write out the expression

`x^2_{}+\text{ 22x}`

Write out the formula to obtain the term that would be added to make it a perfect square trinomial

`b^2-4ac=\text{ 0}`

Write out the data given to obtain "C"

`\begin{gathered} \text{Comparing the expression with the equation written below} \\ ax^2+bx+c=0 \\ \text{where a=1 (coefficient of x}^2) \\ b=\text{ 22 (coefficient of x)} \\ c=\text{ unknown we are looking for} \end{gathered}`

Obtaining for the value of "c"

`\begin{gathered} 22^2-4(1)(c)=\text{ 0} \\ 484-\text{ 4c= 0} \\ \text{ Collect like terms} \\ 484=4c \\ \text{Divide both sides by 4} \\ (484)/(4)=(4c)/(4) \\ 121=c \end{gathered}`

The term that would be added to make it a perfect square trinomial is 121.