Solve Using the Quadratic Formula x^2-11x+30=0

Problem

x2−11*x+30=0

Solution

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

a=1

b=−11

c=30

2. State the quadratic formula.

x=(−b±√(,b2−4*a*c))/(2*a)

3. Substitute the values of a b and c into the formula.

x=(−(−11)±√(,(−11)2−4*(1)*(30)))/(2*(1))

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

x=(11±√(,121−120))/2

x=(11±√(,1))/2

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

x=(11±1)/2

6. Calculate the first solution using the plus sign.

x=(11+1)/2=12/2=6

7. Calculate the second solution using the minus sign.

x=(11−1)/2=10/2=5

Final Answer

x=5,6

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