Solve Using the Quadratic Formula x^2-12x+27=0

Problem

x2−12*x+27=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=−12

c=27

2. State the quadratic formula used to find the roots of the equation.

x=(−b±√(,b2−4*a*c))/(2*a)

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

x=(−(−12)±√(,(−12)2−4*(1)*(27)))/(2*(1))

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

x=(12±√(,144−108))/2

x=(12±√(,36))/2

5. Evaluate the square root and simplify the fraction.

x=(12±6)/2

6. Solve for the two possible values of x by calculating both the addition and subtraction cases.

x=(12+6)/2=18/2=9

x=(12−6)/2=6/2=3

Final Answer

x=9,3

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