Solve Using the Quadratic Formula x^2-10x+41=0

Problem

x2−10*x+41=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=−10

c=41

2. State the quadratic formula used to find the roots of the equation.

x=(−b±√(,b2−4*a*c))/(2*a)

3. Substitute the identified values into the quadratic formula.

x=(−(−10)±√(,(−10)2−4*(1)*(41)))/(2*(1))

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

x=(10±√(,100−164))/2

x=(10±√(,−64))/2

5. Apply the imaginary unit i to handle the square root of the negative number, where √(,−64)=8*i

x=(10±8*i)/2

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

x=5±4*i

Final Answer

x=5±4*i

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