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

Problem

2*x2+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=1

c=−1

2. Apply the quadratic formula to find the values of x

x=(−b±√(,b2−4*a*c))/(2*a)

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

x=(−(1)±√(,(1)2−4*(2)*(−1)))/(2*(2))

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

x=(−1±√(,1+8))/4

x=(−1±√(,9))/4

5. Evaluate the square root.

x=(−1±3)/4

6. Solve for the two possible values of x by calculating both the plus and minus cases.

(x_1)=(−1+3)/4=2/4=1/2

(x_2)=(−1−3)/4=(−4)/4=−1

Final Answer

x=1/2,−1

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