Solve Using the Quadratic Formula 2x^2-x-3=0

Problem

2*x2−x−3=0

Solution

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

a=2

b=−1

c=−3

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=(−(−1)±√(,(−1)2−4*(2)*(−3)))/(2*(2))

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

x=(1±√(,1+24))/4

x=(1±√(,25))/4

5. Evaluate the square root.

x=(1±5)/4

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

(x_1)=(1+5)/4=6/4=3/2

(x_2)=(1−5)/4=(−4)/4=−1

Final Answer

x=3/2,−1

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