Final answer:
The quadratic equation x^2 + 3 = 9x can be solved with the quadratic formula. The solutions, rounded to the nearest hundredth, are x = 0.35 and x = -8.65, which corresponds to choice a.
Step-by-step explanation:
To solve the equation x2 + 3 = 9x using the quadratic formula, first we need to bring all terms to one side of the equation to take the form ax2 + bx + c = 0. Subtracting 9x from both sides gives us:
x2 - 9x + 3 = 0
Now, we can apply the quadratic formula:
x = (-b ± √(b2 - 4ac)) / (2a)
For our equation, a = 1, b = -9, and c = 3. Plugging these values into the formula gives us:
x = (-(-9) ± √((-9)2 - 4(1)(3))) / (2(1))
x = (9 ± √(81 - 12)) / 2
x = (9 ± √(69)) / 2
Calculating the square root and simplifying:
x = (9 ± 8.3066) / 2
So we have two solutions:
- x = (9 + 8.3066) / 2 ≈ 8.65 (Rounded to nearest hundredth)
- x = (9 - 8.3066) / 2 ≈ 0.35 (Rounded to nearest hundredth)
Therefore, the solutions are approximately x = 0.35 and x = -8.65, which matches answer choice a. Remember to always check your solutions in the original equation.