Solve Using the Quadratic Formula x^2-2x-3=0

Problem

x2−2*x−3=0

Solution

1. Identify the coefficients of the quadratic equation in the form a*x2+b*x+c=0

a=1

b=−2

c=−3

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)*(−3)))/(2*(1))

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

x=(2±√(,4+12))/2

x=(2±√(,16))/2

5. Evaluate the square root and simplify the fraction.

x=(2±4)/2

6. Solve for both cases of the plus-minus sign to find the two possible values for x

x=(2+4)/2=6/2=3

x=(2−4)/2=(−2)/2=−1

Final Answer

x=3,−1

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