Step 1 :\( A = (x-2)(3x+4) + 2x^2 - 8 \)
Step 2 :\( A = 3x^2 - 6x + 4x - 8 + 2x^2 - 8 \)
Step 3 :\( A = 5x^2 - 2x - 16 \)
Step 4 :\( A(x=-\sqrt{3}) = 5(-\sqrt{3})^2 - 2(-\sqrt{3}) - 16 \)
Step 5 :\( A(x=-\sqrt{3}) = 5(3) + 2\sqrt{3} - 16 \)
Step 6 :\( A(x=-\sqrt{3}) = 7 + 2\sqrt{3} \)
Step 7 :\( A(x=\frac{1}{2}) = 5\left(\frac{1}{2}\right)^2 - 2\left(\frac{1}{2}\right) - 16 \)
Step 8 :\( A(x=\frac{1}{2}) = 5\left(\frac{1}{4}\right) - 1 - 16 \)
Step 9 :\( A(x=\frac{1}{2}) = -\frac{11}{4} \)
Step 10 :\( 2x^2 - 8 = (2x+4)(x-2) \)
Step 11 :\( A = (x-2)[(2x+4)(x-2)] \)
Step 12 :\( A = (x-2)(5x+8) \)
Step 13 :\( (x-2)(5x+8) = 0 \)
Step 14 :\( \Rightarrow x = 2, \frac{-8}{5} \)