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:

⚡ Using what you learned: quadratic formula and its applications

Step 1: Identify the coefficients

For the quadratic equation \( 0.25x^2 - 8x = 0 \), compare it to the standard form \( ax^2 + bx + c = 0 \):

$$ a = 0.25 $$

$$ b = -8 $$

$$ c = 0 $$

Step 2: Substitute into the quadratic formula

The quadratic formula is:

$$ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} $$

Substitute the values of \( a \), \( b \), and \( c \):

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

Simplify the leading term \( -(-8) \):

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

Answer:

The correct equation is the third option:

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