Solve Using the Quadratic Formula x^2-6x-3=0

Problem

x2−6*x−3=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=−6

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=(−(−6)±√(,(−6)2−4*(1)*(−3)))/(2*(1))

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

x=(6±√(,36+12))/2

x=(6±√(,48))/2

5. Simplify the radical by factoring out the largest perfect square.

√(,48)=√(,16⋅3)=4√(,3)

x=(6±4√(,3))/2

6. Divide each term in the numerator by the denominator to find the final values of x

x=3±2√(,3)

Final Answer

x=3±2√(,3)

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