Solve Using the Quadratic Formula x^2-10x+29=0

Problem

x2−10*x+29=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=29

2. Apply the formula for the quadratic equation, which is x=(−b±√(,b2−4*a*c))/(2*a)

x=(−(−10)±√(,(−10)2−4*(1)*(29)))/(2*(1))

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

x=(10±√(,100−116))/2

x=(10±√(,−16))/2

4. Evaluate the square root of the negative number using the imaginary unit i where √(,−16)=4*i

x=(10±4*i)/2

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

x=5±2*i

Final Answer

x=5±2*i

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