Solve Using the Quadratic Formula 9x^2+16=0

Problem

9*x2+16=0

Solution

1. Identify the coefficients for the quadratic equation in the form a*x2+b*x+c=0

a=9

b=0

c=16

2. Substitute these values into the quadratic formula.

x=(−b±√(,b2−4*a*c))/(2*a)

x=(−0±√(,0−4*(9)*(16)))/(2*(9))

3. Simplify the expression inside the square root, also known as the discriminant.

x=(±√(,−576))/18

4. Apply the imaginary unit i to handle the square root of the negative number, since √(,−576)=√(,576)⋅√(,−1)=24*i

x=(±24*i)/18

5. Reduce the fraction by dividing the numerator and the denominator by their greatest common divisor, which is 6

x=±(4*i)/3

Final Answer

x=±4/3*i

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