Solve Using the Quadratic Formula x^2-2x-8=0

Problem

x2−2*x−8=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=−8

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)*(−8)))/(2*(1))

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

x=(2±√(,4+32))/2

x=(2±√(,36))/2

5. Evaluate the square root and simplify the fraction.

x=(2±6)/2

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

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

x=(2−6)/2=(−4)/2=−2

Final Answer

x=4,−2

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