Question

quiz instructions

for this quiz, answer each question and either select the best option or use the drop-downs.

for answers that are typed into the box, separate multiple answers with a comma.

you have 20 minutes to complete the quiz.

you have only one attempt.

question 1

solve the equation with the quadratic formula. type your answer. fractional quantities can be typed using /.

(4v^2 + 1 = -5v)

(v = \\{\quad\\}\\)

Explanation:

⚡ Using what you learned: quadratic formula and its applications

Step 1: Standard Form

Rearrange the equation into standard form \( av^2 + bv + c = 0 \):

$$ 4v^2 + 5v + 1 = 0 $$

Here, \( a = 4 \), \( b = 5 \), and \( c = 1 \).

Step 2: Apply Quadratic Formula

Substitute the coefficients into the quadratic formula \( v = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \):

$$ v = \frac{-5 \pm \sqrt{5^2 - 4(4)(1)}}{2(4)} $$

$$ v = \frac{-5 \pm \sqrt{25 - 16}}{8} $$

$$ v = \frac{-5 \pm \sqrt{9}}{8} $$

$$ v = \frac{-5 \pm 3}{8} $$

Step 3: Solve for Both Values

Calculate the two possible values for \( v \):

$$ v_1 = \frac{-5 + 3}{8} = \frac{-2}{8} = -\frac{1}{4} $$

$$ v_2 = \frac{-5 - 3}{8} = \frac{-8}{8} = -1 $$

Answer:

-1, -1/4