Question

choose the equation that represents the solutions of $0 = 0.25x^{2}-8x$
$x = \frac{0.25\pm\sqrt{(0.25)^{2}-(4)(1)(-8)}}{2(1)}$
$x = \frac{-0.25\pm\sqrt{(0.25)^{2}-(4)(1)(-8)}}{2(1)}$
$x = \frac{8\pm\sqrt{(-8)^{2}-(4)(0.25)(0)}}{2(0.25)}$
$x = \frac{-8\pm\sqrt{(-8)^{2}-(4)(0.25)(0)}}{2(0.25)}$

Explanation:

Step1: Recall quadratic formula

For $ax^2+bx+c=0$, $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Step2: Identify a, b, c values

From $0.25x^2-8x=0$, $a=0.25$, $b=-8$, $c=0$

Step3: Substitute into formula

$x=\frac{-(-8)\pm\sqrt{(-8)^2-4(0.25)(0)}}{2(0.25)}=\frac{8\pm\sqrt{(-8)^2-(4)(0.25)(0)}}{2(0.25)}$

Answer:

$\boldsymbol{x=\frac{8\pm\sqrt{(-8)^2-(4)(0.25)(0)}}{2(0.25)}}$ (the third option)