Final answer:
To solve the equation 4v² + 3 = -8v, we can use the quadratic formula. The solutions for v are -1 and -0.5.
Step-by-step explanation:
To solve the equation 4v² + 3 = -8v for v, we need to set the equation to zero by moving all terms to one side. Start by adding 8v to both sides to get 4v² + 8v + 3 = 0. Now, this is a quadratic equation, so we can solve it by factoring, completing the square, or using the quadratic formula. In this case, we'll use the quadratic formula: v = (-b ± √(b² - 4ac)) / (2a). Plugging in the values a = 4, b = 8, and c = 3, we get v = (-8 ± √(8² - 4(4)(3))) / (2(4)). Simplifying further, we have v = (-8 ± √(64 - 48)) / 8, which gives us v = (-8 ± √16) / 8. Finally, v = (-8 ± 4) / 8, so the two solutions for v are v = -1 and v = -0.5.