Solve Using the Quadratic Formula x^2+9x+14=0

Problem

x2+9*x+14=0

Solution

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

a=1

b=9

c=14

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*(1)*(14)))/(2*(1))

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

x=(−9±√(,81−56))/2

x=(−9±√(,25))/2

5. Evaluate the square root.

x=(−9±5)/2

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

(x_1)=(−9+5)/2=(−4)/2=−2

(x_2)=(−9−5)/2=(−14)/2=−7

Final Answer

x=−2,−7

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