Solve Using the Quadratic Formula 14x^2+3x-2=0

Problem

14*x2+3*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=14

b=3

c=−2

2. Apply the quadratic formula by substituting the identified values into the formula x=(−b±√(,b2−4*a*c))/(2*a)

x=(−3±√(,3−4*(14)*(−2)))/(2*(14))

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

x=(−3±√(,9+112))/28

x=(−3±√(,121))/28

4. Evaluate the square root and solve for the two possible values of x

x=(−3±11)/28

5. Calculate the first solution using the plus sign.

x=(−3+11)/28

x=8/28

x=2/7

6. Calculate the second solution using the minus sign.

x=(−3−11)/28

x=(−14)/28

x=−1/2

Final Answer

x=2/7,−1/2

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