Solve Using the Quadratic Formula x^2+64=0

Problem

x2+64=0

Solution

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

a=1

b=0

c=64

2. Apply the quadratic formula to find the values of x

x=(−b±√(,b2−4*a*c))/(2*a)

3. Substitute the values of a b and c into the formula.

x=(−0±√(,0−4*(1)*(64)))/(2*(1))

4. Simplify the expression under the square root (the discriminant).

x=(±√(,−256))/2

5. Evaluate the square root of the negative number using the imaginary unit i where √(,−1)=i

x=(±16*i)/2

6. Divide to find the final solutions.

x=±8*i

Final Answer

x=±8*i

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