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

Problem

x2−2*x−5=0

Solution

1. Identify the coefficients a b and c from the standard form a*x2+b*x+c=0

a=1

b=−2

c=−5

2. State the quadratic formula.

x=(−b±√(,b2−4*a*c))/(2*a)

3. Substitute the values of a b and c into the formula.

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

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

x=(2±√(,4+20))/2

x=(2±√(,24))/2

5. Simplify the radical by factoring out the largest perfect square.

x=(2±√(,4⋅6))/2

x=(2±2√(,6))/2

6. Divide each term in the numerator by the denominator to find the final values of x

x=1±√(,6)

Final Answer

x=1±√(,6)

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