Solve Using the Quadratic Formula x^2-4x-12=0

Problem

x2−4*x−12=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=−4

c=−12

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

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

x=(4±√(,16+48))/2

x=(4±√(,64))/2

5. Evaluate the square root and simplify the fraction.

x=(4±8)/2

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

x=(4+8)/2=12/2=6

x=(4−8)/2=(−4)/2=−2

Final Answer

x=6,−2

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