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

Problem

x2−5*x−2=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=−2

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 of a b and c into the formula.

x=(−(−5)±√(,(−5)2−4*(1)*(−2)))/(2*(1))

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

x=(5±√(,25+8))/2

x=(5±√(,33))/2

5. Separate the expression into the two possible solutions for x

x=(5+√(,33))/2

x=(5−√(,33))/2

Final Answer

x=(5±√(,33))/2

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