Solve Using the Quadratic Formula x^2-11x+28=0

Problem

x2−11*x+28=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=28

2. Apply the quadratic formula by substituting the identified values into the formula x=(−b±√(,b2−4*a*c))/(2*a)

x=(−(−11)±√(,(−11)2−4*(1)*(28)))/(2*(1))

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

x=(11±√(,121−112))/2

x=(11±√(,9))/2

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

x=(11±3)/2

5. Calculate the two distinct solutions.

(x_1)=(11+3)/2=14/2=7

(x_2)=(11−3)/2=8/2=4

Final Answer

x=7,4

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