Final answer:
The quadratic equation 9m² + m - 4 = 0 is solved using the quadratic formula. The solutions are m = 0.614 and m = -0.724 when rounded to the nearest hundredth.
Step-by-step explanation:
To solve the quadratic equation: 9m² + m - 4 = 0, we can apply the quadratic formula, which is x = (-b ± √(b² - 4ac)) / (2a). For our equation, a = 9, b = 1, and c = -4. Plugging these values into the formula, we find:
- m = (-1 ± √(1² - 4(9)(-4))) / (2 * 9)
- m = (-1 ± √(1 + 144)) / 18
- m = (-1 ± √(145)) / 18
- m = (-1 ± 12.0416) / 18
- m = (-1 + 12.0416) / 18 or m = (-1 - 12.0416) / 18
- m = 11.0416 / 18 or m = -13.0416 / 18
- m = 0.614 or m = -0.724
The answers are integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.