Solve Using the Quadratic Formula x^2-6x+34=0

Problem

x2−6*x+34=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=34

2. Substitute these values into the quadratic formula.

x=(−b±√(,b2−4*a*c))/(2*a)

x=(−(−6)±√(,(−6)2−4*(1)*(34)))/(2*(1))

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

x=(6±√(,36−136))/2

x=(6±√(,−100))/2

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

√(,−100)=10*i

x=(6±10*i)/2

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

x=3±5*i

Final Answer

x=3±5*i

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