Question

solve using the quadratic formula.
5v² - 7v - 4 = 0
write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.
v = or v =
submit

Explanation:

Step1: Identify a, b, c values

For $5v^2 - 7v - 4 = 0$, $a=5$, $b=-7$, $c=-4$

Step2: Recall quadratic formula

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

Step3: Calculate discriminant

$\Delta = (-7)^2 - 4(5)(-4) = 49 + 80 = 129$

Step4: Substitute into formula

$$v = \frac{7 \pm \sqrt{129}}{10}$$

Step5: Compute decimal values

$\sqrt{129} \approx 11.3578$, so:
$v_1 = \frac{7 + 11.3578}{10} \approx 1.84$, $v_2 = \frac{7 - 11.3578}{10} \approx -0.44$

Answer:

$v = \frac{7 + \sqrt{129}}{10}$ or $v = \frac{7 - \sqrt{129}}{10}$
(or as decimals: $v \approx 1.84$ or $v \approx -0.44$)