Question

(1/2)x^2 = 2x^2 -4x + 8x -16

Answer 1

$\left(\dfrac{1}{2}\right)x^2=2x^2-4x+8x-16$

$\dfrac{1}{2}x^2=2x^2+4x-16$

$2x^2+4x-16=\dfrac{1}{2}x^2$

$2x^2+4x-16-\dfrac{1}{2}x^2=\dfrac{1}{2}x^2-\dfrac{1}{2}x^2$

$\dfrac{3x^2}{2}+4x-16=0$

$x_{1,\:2}=\dfrac{-4\pm \sqrt{4^2-4\cdot \frac{3}{2}\left(-16\right)}}{2\cdot \frac{3}{2}}$

$x_{1,\:2}=\dfrac{-4\pm \:4\sqrt{7}}{2\cdot \frac{3}{2}}$

$x_1=\dfrac{-4+4\sqrt{7}}{2\cdot \frac{3}{2}},\:x_2=\dfrac{-4-4\sqrt{7}}{2\cdot \frac{3}{2}}$

$x=\dfrac{-4+4\sqrt{7}}{3},\:x=\dfrac{-4-4\sqrt{7}}{3}$