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Sagot :
Answer:
Question:
The expression is given below as
[tex]\begin{gathered} x^2+18x+k \\ let\text{ }k=missing\text{ number} \end{gathered}[/tex]Concept:
The general expression of a quadratic expression is given below as
[tex]ax^2+bx+c[/tex]By comparing coefficients, we will have
[tex]\begin{gathered} x^2+18x+k \\ ax^2+bx+c \\ a=1,b=18,c=k \end{gathered}[/tex]The formula to be used to calculate the number to make a quadratic expression a perfect square
[tex]\begin{gathered} b^2=4ac \\ b^2=4ak \\ k=\frac{b^2}{4a} \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} k=\frac{b^{2}}{4a},b=18,a=1 \\ k=\frac{18^2}{4\times1} \\ k=\frac{324}{4} \\ k=81 \end{gathered}[/tex]Hence,
The final answer is
[tex]\Rightarrow81[/tex]
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