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Complete the square. x2 + 18x + 90 = 0

User Yrahman
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1 Answer

3 votes

we have the equation


x^2+18x+90=0

Complete the square


\begin{gathered} (x^2+18x)+90=0 \\ (x^2+18x+9^2-9^2)+90=0 \\ (x^2+18x+9^2)+90-9^2=0 \\ (x^2+18x+81)+9=0 \end{gathered}

Rewrite as perfect squares


\begin{gathered} (x+9)^2+9=0 \\ (x+9)^2=-9 \end{gathered}

take square root both sides


√((x+9)^2)=\pm√(-9)
\begin{gathered} x+9=\pm3i \\ x=-9\pm3i \end{gathered}

User Boriana Ditcheva
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