Solve Using the Quadratic Formula x^2+5x+6=0

Problem

x2+5*x+6=0

Solution

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

a=1

b=5

c=6

2. Apply the quadratic formula which is given by x=(−b±√(,b2−4*a*c))/(2*a)

x=(−5±√(,5−4*(1)*(6)))/(2*(1))

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

x=(−5±√(,25−24))/2

x=(−5±√(,1))/2

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

x=(−5±1)/2

5. Calculate the first solution using the plus sign.

(x_1)=(−5+1)/2=(−4)/2=−2

6. Calculate the second solution using the minus sign.

(x_2)=(−5−1)/2=(−6)/2=−3

Final Answer

x=−2,−3

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