Question

Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth. x2 + 3 = 9x a 0.35, -8.65 b -0.35, -8.65 c -0.35, 8.65 d 0.35, 8.65

Answer 1

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.

Answer 2

1. You have the following quadratic equation and to solve it, you must follow the steps below:

x²+3=9x

2. The form of the equation that you need to apply the quadratic formula, is:

ax²+bx+c=0

3. Then:

x²+3=9x
x²-9x+3=0

4. The quadratic formula is shown below:

x=(-b±√(b^2-4ac))/2a

5. Then, you have:

a=1
b=-9
c=3

6. When you substitute the values into the quadratic formula, you obtain:

x1=0.34
x2=8.65