Question

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

Explanation:

Step1: Identify quadratic coefficients

For $0=0.25x^2 -8x$, standard form is $ax^2+bx+c=0$, so $a=0.25$, $b=-8$, $c=0$.

Step2: Recall quadratic formula

The quadratic formula is $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$.

Step3: Substitute coefficients into formula

Substitute $a=0.25$, $b=-8$, $c=0$:
$x=\frac{-(-8)\pm\sqrt{(-8)^2-(4)(0.25)(0)}}{2(0.25)}=\frac{8\pm\sqrt{(-8)^2-(4)(0.25)(0)}}{2(0.25)}$

Answer:

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