Solve Using the Quadratic Formula x^2-5x+7=0

Problem

x2−5*x+7=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=−5

c=7

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=(−(−5)±√(,(−5)2−4*(1)*(7)))/(2*(1))

4. Simplify the expression under the square root, which is the discriminant.

x=(5±√(,25−28))/2

x=(5±√(,−3))/2

5. Apply the definition of the imaginary unit i=√(,−1) to handle the square root of the negative number.

x=(5±i√(,3))/2

Final Answer

x=(5±i√(,3))/2

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