Solve Using the Quadratic Formula x^2-2x-15=0

Problem

x2−2*x−15=0

Solution

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

a=1

b=−2

c=−15

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)*(−15)))/(2*(1))

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

x=(2±√(,4+60))/2

x=(2±√(,64))/2

5. Evaluate the square root and simplify the fraction.

x=(2±8)/2

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

x=(2+8)/2=10/2=5

x=(2−8)/2=(−6)/2=−3

Final Answer

x=5,−3

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