Question

What are the solutions?
16x2 + 9 = 0

Answer 1

I don't really understand

Answer 2

To find the solutions, we need to solve the equation 16x^2 + 9 = 0.

First, we need to move the constant term to the other side:
16x^2 = -9

Next, we divide both sides by 16 to isolate the variable:
x^2 = -9/16

To solve for x, we take the square root of both sides, considering both the positive and negative square root:
x = ±√(-9/16)

Since we cannot take the square root of a negative number within the real number system, this equation has no real solutions. However, in the complex number system, the square root of a negative number can be represented by the imaginary unit i. Thus, the two complex solutions to the equation are:
x = ±(3i/4)

Answer 3

I apologize for the confusion. Let's go through the steps again with more detail.

We are given the equation 16x^2 + 9 = 0. To find the solutions, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac))/(2a)

In this equation, a, b, and c correspond to the coefficients of the quadratic equation ax^2 + bx + c = 0.

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

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

Simplifying further:

x = (± √(0 - 576))/(32)
x = (± √(-576))/(32)

Now, we can simplify the square root of -576. The square root of a negative number is not a real number. However, we can express it using the imaginary unit i, which is defined as √(-1).

√(-576) = √(576 * -1) = √(-1) * √(576) = i * 24 = 24i

Plugging this back into the equation, we have:

x = (± 24i)/(32)

Simplifying further:

x = ± (24i)/(32)

Next, we can simplify the fraction:

x = ± (6i)/(8)

Further simplifying:

x = ± (3i)/(4)

Therefore, the solutions to the equation 16x^2 + 9 = 0 are x = (3i)/(4) and x = (-3i)/(4). These are complex solutions, as they include the imaginary unit i.