Select the approximate values of x that are solutions to f(x) = 0, where f(x) = -2x^2 + 9x + 9.

a) {–0.22, 1.00}

b) {-2, 9}

c) {–4.50, –4.50}

d) {–0.84, 5.34}

looks like (D) to me

thank you Steve

To find the approximate values of x that are solutions to f(x) = 0, we need to solve the quadratic equation -2x^2 + 9x + 9 = 0. There are several methods to solve this equation, but one commonly used method is the quadratic formula.

The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for x are given by:

x = (-b ± √(b^2 - 4ac)) / 2a

In this case, a = -2, b = 9, and c = 9. Plugging these values into the quadratic formula, we get:

x = (-9 ± √(9^2 - 4(-2)(9))) / (2(-2))
x = (-9 ± √(81 + 72)) / -4
x = (-9 ± √153) / -4

To find the approximate values of x, we need to calculate the square root of 153 and compute the two possible solutions.

Using a calculator or a math software, we find that √153 ≈ 12.37.

Now we can calculate the two solutions:

x1 = (-9 + 12.37) / -4 ≈ -0.84
x2 = (-9 - 12.37) / -4 ≈ 5.34

So the approximate values of x that are solutions to f(x) = 0 are {–0.84, 5.34}.

Therefore, the correct answer is d) {–0.84, 5.34}.