Final answer:
To solve the quadratic equation 3x²-8x-14=0, the quadratic formula is used to find two solutions, which to the nearest tenth are x ≈ 3.9 and x ≈ -1.2.
Step-by-step explanation:
To solve the equation 3x²-8x-14=0 to the nearest tenth, we use the quadratic formula, which is √(b² - 4ac) / (2a), where a=3, b=-8, and c=-14. Substituting these values into the formula, we get:
x = (-(-8) ± √((-8)² - 4 * 3 * (-14))) / (2 * 3)
= (8 ± √(64 + 168)) / 6
= (8 ± √(232)) / 6
Calculating the square root of 232 gives us approximately 15.23. Thus, we get:
x = (8 ± 15.23) / 6
There are two solutions for x:
x = (8 + 15.23) / 6 ≈ 3.9
x = (8 - 15.23) / 6 ≈ -1.2
Therefore, the solutions to the equation to the nearest tenth are x ≈ 3.9 and x ≈ -1.2.