Solve Using the Quadratic Formula x^2+11x=-28

Problem

x2+11*x=−28

Solution

1. Rearrange the equation into standard form a*x2+b*x+c=0 by adding 28 to both sides.

x2+11*x+28=0

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

a=1

b=11

c=28

3. Substitute the coefficients into the quadratic formula x=(−b±√(,b2−4*a*c))/(2*a)

x=(−11±√(,11−4*(1)*(28)))/(2*(1))

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

x=(−11±√(,121−112))/2

x=(−11±√(,9))/2

5. Evaluate the square root.

x=(−11±3)/2

6. Solve for both possible values of x

x=(−11+3)/2=(−8)/2=−4

x=(−11−3)/2=(−14)/2=−7

Final Answer

x=−4,−7

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