Solve Using the Quadratic Formula 5x^2=-12x-2

Problem

5*x2=−12*x−2

Solution

1. Rearrange the equation into standard form a*x2+b*x+c=0 by adding 12*x and 2 to both sides.

5*x2+12*x+2=0

2. Identify the coefficients a b and c for the quadratic formula.

a=5

b=12

c=2

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

x=(−12±√(,12−4*(5)*(2)))/(2*(5))

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

x=(−12±√(,144−40))/10

x=(−12±√(,104))/10

5. Simplify the radical by factoring out the largest perfect square from 104

√(,104)=√(,4⋅26)=2√(,26)

x=(−12±2√(,26))/10

6. Reduce the fraction by dividing the numerator and denominator by their greatest common factor, which is 2

x=(2*(−6±√(,26)))/10

x=(−6±√(,26))/5

Final Answer

x=(−6±√(,26))/5

Want more problems? Check here!