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
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.
To solve the equation 16x^2 + 9 = 0, we need to find the values of x that satisfy the equation. Let's go through the steps to find the solutions.
Step 1: Move the constant term to the other side of the equation.
16x^2 = -9
Step 2: Divide both sides of the equation by the coefficient of x^2 to isolate the x^2 term.
x^2 = -9/16
Step 3: Take the square root of both sides of the equation to solve for x.
There are two possible solutions since we have a square root.
x = ±√(-9/16)
Simplifying the square root of a negative number, we can rewrite it as the imaginary unit, "i".
x = ±√(-1) * √(9/16)
Step 4: Simplify the square root expression.
x = ± (3/4) * i
Therefore, the solutions to the equation 16x^2 + 9 = 0 are:
x = (3/4) * i
and
x = -(3/4) * i
Note: The response options you provided in your question are incorrect. The correct solutions are ±(3/4) * i.
To solve the equation 16x^2 + 9 = 0, we can use the quadratic formula.
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this equation, a = 16, b = 0, and c = 9.
Plugging in the values, we get:
x = (0 ± √(0^2 - 4 * 16 * 9)) / (2 * 16)
x = (0 ± √(-576)) / 32
Since the expression inside the square root (√(-576)) is negative, the solutions will involve the imaginary unit "i". Therefore, the solutions to the equation 16x^2 + 9 = 0 are "±i".