Solve Using the Quadratic Formula 2x^2-5x-1=0

Problem

2*x2−5*x−1=0

Solution

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

a=2

b=−5

c=−1

2. State the quadratic formula used to find the roots of the equation.

x=(−b±√(,b2−4*a*c))/(2*a)

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

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

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

x=(5±√(,25+8))/4

x=(5±√(,33))/4

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

x=(5+√(,33))/4

x=(5−√(,33))/4

Final Answer

x=(5±√(,33))/4

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