What are the solutions? 16x2 + 9 = 0 (1 point) Responses –i, i – Image with alt text: 3 over 4 i, Image with alt text: 3 over 4 i –i, i – Image with alt text: 4 over 3 i, Image with alt text: 4 over 3 i – , – Image with alt text: 3 over 4 , Image with alt text: 3 over 4 –i, i

Answer 1

To solve the equation 16x^2 + 9 = 0, you can use the quadratic formula.

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

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 16, b = 0, and c = 9. Substituting these values into the quadratic formula:

x = (0 ± √(0^2 - 4(16)(9))) / (2(16))
x = (0 ± √(-576)) / 32

Since the term inside the square root is negative, the solutions will be complex numbers.

Using the imaginary unit, i, which is defined as √(-1), the solutions can be written as:

x = ± (√576) / 32
x = ± (24) / 32

Simplifying further:

x = ± 3/4

The solutions to the equation 16x^2 + 9 = 0 are x = 3/4i and x = -3/4i.