Solve Using the Quadratic Formula x^2-12x+32=0

Problem

x2−12*x+32=0

Solution

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

a=1

b=−12

c=32

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

x=(−(−12)±√(,(−12)2−4*(1)*(32)))/(2*(1))

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

x=(12±√(,144−128))/2

x=(12±√(,16))/2

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

x=(12±4)/2

5. Calculate the first solution using the plus sign.

x=(12+4)/2=16/2=8

6. Calculate the second solution using the minus sign.

x=(12−4)/2=8/2=4

Final Answer

x=8,4

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