Solve Using the Quadratic Formula x^2-4x+13=0

Problem

x2−4*x+13=0

Solution

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

a=1

b=−4

c=13

2. Apply the quadratic formula which is given by x=(−b±√(,b2−4*a*c))/(2*a)

x=(−(−4)±√(,(−4)2−4*(1)*(13)))/(2*(1))

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

x=(4±√(,16−52))/2

x=(4±√(,−36))/2

4. Evaluate the square root of the negative number using the imaginary unit i where √(,−36)=6*i

x=(4±6*i)/2

5. Divide each term in the numerator by the denominator to find the final complex solutions.

x=2±3*i

Final Answer

x=2±3*i

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