Solve Using the Quadratic Formula x^2-11x+18=0

Problem

x2−11*x+18=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=−11

c=18

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)2−4*(1)*(18)))/(2*(1))

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

x=(11±√(,121−72))/2

x=(11±√(,49))/2

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

x=(11±7)/2

6. Calculate the first solution using the addition.

(x_1)=(11+7)/2=18/2=9

7. Calculate the second solution using the subtraction.

(x_2)=(11−7)/2=4/2=2

Final Answer

x=9,2

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