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 quadratic equation in standard form a*x2+b*x+c=0

a=1

b=12

c=32

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=(−12±√(,12−4*(1)*(32)))/(2*(1))

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

x=(−12±√(,144−128))/2

x=(−12±√(,16))/2

5. Evaluate the square root and split the equation into two possible solutions for x

x=(−12±4)/2

6. Calculate the first solution using the plus sign.

x=(−12+4)/2

x=(−8)/2

x=−4

7. Calculate the second solution using the minus sign.

x=(−12−4)/2

x=(−16)/2

x=−8

Final Answer

x=−4,−8

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