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Solve the following.
Solve for x: |1 -2 5; 2 x -1; 0 4 2x| = 86.
Solve for $x$:
$\begin{vmatrix} 1 & -2 & 5 \\ 2 & x & -1 \\ 0 & 4 & 2x \end{vmatrix} = 86$.
Answer
Answer
Expanding along $R_1$: $1(2x^2 + 4) + 2(4x - 0) + 5(8 - 0) = 2x^2 + 8x + 44$.
$2x^2 + 8x + 44 = 86 \Rightarrow x^2 + 4x - 21 = 0 \Rightarrow (x+7)(x-3) = 0$.
Final answer: $x = 3, -7$