Solve Using the Quadratic Formula x^2+2x-48=0

Problem

x2+2*x−48=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=2

c=−48

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=(−(2)±√(,(2)2−4*(1)*(−48)))/(2*(1))

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

x=(−2±√(,4+192))/2

x=(−2±√(,196))/2

5. Evaluate the square root of 196

x=(−2±14)/2

6. Solve for the two possible values of x by calculating the plus and minus cases separately.

x=(−2+14)/2=12/2=6

x=(−2−14)/2=(−16)/2=−8

Final Answer

x=6,−8

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