Solve Using the Quadratic Formula x^2-8x+20=0

Problem

x2−8*x+20=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=−8

c=20

2. Apply the quadratic formula to find the values of x

x=(−b±√(,b2−4*a*c))/(2*a)

3. Substitute the values of a b and c into the formula.

x=(−(−8)±√(,(−8)2−4*(1)*(20)))/(2*(1))

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

x=(8±√(,64−80))/2

x=(8±√(,−16))/2

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

x=(8±4*i)/2

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

x=4±2*i

Final Answer

x=4±2*i

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