Solve Using the Quadratic Formula x^2-6x+13=0

Problem

x2−6*x+13=0

Solution

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

a=1

b=−6

c=13

2. Substitute these values into the quadratic formula.

x=(−b±√(,b2−4*a*c))/(2*a)

x=(−(−6)±√(,(−6)2−4*(1)*(13)))/(2*(1))

3. Simplify the expression under the square root, known as the discriminant.

x=(6±√(,36−52))/2

x=(6±√(,−16))/2

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

√(,−16)=4*i

x=(6±4*i)/2

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

x=3±2*i

Final Answer

x2−6*x+13=0⇒x=3±2*i

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