Solve Using the Quadratic Formula x^2-8x+25=0

Problem

x2−8*x+25=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=25

2. Apply the quadratic formula by substituting the identified values into the formula x=(−b±√(,b2−4*a*c))/(2*a)

x=(−(−8)±√(,(−8)2−4*(1)*(25)))/(2*(1))

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

x=(8±√(,64−100))/2

x=(8±√(,−36))/2

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

√(,−36)=6*i

x=(8±6*i)/2

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

x=4±3*i

Final Answer

x=4±3*i

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