Solve Using the Quadratic Formula x^2+81=0

Problem

x2+81=0

Solution

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

a=1

b=0

c=81

2. Apply the formula for the quadratic equation x=(−b±√(,b2−4*a*c))/(2*a)

x=(−0±√(,0−4*(1)*(81)))/(2*(1))

3. Simplify the expression inside the square root.

x=(±√(,−324))/2

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

√(,−324)=√(,324)⋅√(,−1)

√(,−324)=18*i

5. Solve for x by dividing by the denominator.

x=(±18*i)/2

x=±9*i

Final Answer

x=±9*i

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