Solve Using the Quadratic Formula x^2-2x-6=0

Problem

x2−2*x−6=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=−2

c=−6

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

x=(−(−2)±√(,(−2)2−4*(1)*(−6)))/(2*(1))

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

x=(2±√(,4+24))/2

x=(2±√(,28))/2

4. Simplify the radical by factoring out the largest perfect square from 28.

x=(2±√(,4⋅7))/2

x=(2±2√(,7))/2

5. Divide both terms in the numerator by the denominator to find the final values of x

x=1±√(,7)

Final Answer

x=1±√(,7)

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