Solve Using the Quadratic Formula x^2+11x+24=0

Problem

x2+11*x+24=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=11

c=24

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=(−11±√(,11−4*(1)*(24)))/(2*(1))

4. Simplify the expression inside the square root, which is the discriminant.

x=(−11±√(,121−96))/2

x=(−11±√(,25))/2

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

x=(−11±5)/2

6. Calculate the first solution using the plus sign.

x=(−11+5)/2

x=(−6)/2

x=−3

7. Calculate the second solution using the minus sign.

x=(−11−5)/2

x=(−16)/2

x=−8

Final Answer

x=−3,−8

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