Answer:
To solve the equation 3x² + 16x + 5 = 0, we can use the quadratic formula. The quadratic formula is a formula that provides the solutions for any quadratic equation in the form ax² + bx + c = 0, where a, b, and c are constants.
The quadratic formula states that for an equation of the form ax² + bx + c = 0, the solutions for x can be found using the following formula:
x = (-b ± √(b² - 4ac)) / (2a)
In our given equation, we have a = 3, b = 16, and c = 5. Plugging these values into the quadratic formula, we get:
x = (-16 ± √(16² - 4 * 3 * 5)) / (2 * 3)
Simplifying further:
x = (-16 ± √(256 - 60)) / 6
x = (-16 ± √196) / 6
x = (-16 ± 14) / 6
This gives us two possible solutions for x:
1. x = (-16 + 14) / 6 = -2 / 6 = -1/3
2. x = (-16 - 14) / 6 = -30 / 6 = -5
Therefore, the solutions to the equation 3x² + 16x + 5 = 0 are x = -1/3 and x = -5.