Question

Fill in the blank with a number to make the expression a perfect square.x²+18x+

Answer 1

Question:

The expression is given below as

`\begin{gathered} x^2+18x+k \\ let\text{ }k=missing\text{ number} \end{gathered}`

Concept:

The general expression of a quadratic expression is given below as

`ax^2+bx+c`

By comparing coefficients, we will have

`\begin{gathered} x^2+18x+k \\ ax^2+bx+c \\ a=1,b=18,c=k \end{gathered}`

The formula to be used to calculate the number to make a quadratic expression a perfect square

`\begin{gathered} b^2=4ac \\ b^2=4ak \\ k=(b^2)/(4a) \end{gathered}`

By substituting the values, we will have

`\begin{gathered} k=(b^(2))/(4a),b=18,a=1 \\ k=(18^2)/(4*1) \\ k=(324)/(4) \\ k=81 \end{gathered}`

Hence,

The final answer is

`\Rightarrow81`