Solve Using the Quadratic Formula 5x^2+9x-2=0

Problem

5*x2+9*x−2=0

Solution

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

a=5

b=9

c=−2

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

x=(−b±√(,b2−4*a*c))/(2*a)

3. Substitute the identified values into the quadratic formula.

x=(−9±√(,9−4*(5)*(−2)))/(2*(5))

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

x=(−9±√(,81+40))/10

x=(−9±√(,121))/10

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

x=(−9±11)/10

6. Calculate the first solution using the plus sign.

x=(−9+11)/10

x=2/10

x=1/5

7. Calculate the second solution using the minus sign.

x=(−9−11)/10

x=(−20)/10

x=−2

Final Answer

x=1/5,−2

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