Let's start by analyzing the given quadratic equation: [tex]\(0 = 0.25x^2 - 8x\)[/tex]. This equation is in the standard quadratic form [tex]\(ax^2 + bx + c = 0\)[/tex].
Here, we have:
- [tex]\(a = 0.25\)[/tex]
- [tex]\(b = -8\)[/tex]
- [tex]\(c = 0\)[/tex]
We use the quadratic formula to find the roots of the equation:
[tex]\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]
Substituting in the values for [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex]:
1. Calculate the discriminant [tex]\(b^2 - 4ac\)[/tex]:
[tex]\[ b^2 - 4ac = (-8)^2 - 4(0.25)(0) = 64 - 0 = 64 \][/tex]
2. Substitute [tex]\(b\)[/tex], the discriminant, [tex]\(a\)[/tex], and [tex]\(c\)[/tex] into the quadratic formula:
[tex]\[ x = \frac{-(-8) \pm \sqrt{64}}{2(0.25)} \][/tex]
[tex]\[ x = \frac{8 \pm \sqrt{64}}{0.5} \][/tex]
Hence, the correct equation that represents the solutions of [tex]\(0 = 0.25x^2 - 8x\)[/tex] is:
[tex]\[ x = \frac{8 \pm \sqrt{(-8)^2 - (4)(0.25)(0)}}{2(0.25)} \][/tex]
Thus, the correct choice is:
[tex]\[ x = \frac{8 \pm \sqrt{(-8)^2 - (4)(0.25)(0)}}{2(0.25)} \][/tex]
