Solve Using the Quadratic Formula x^2+6x-1=0

Problem

x2+6*x−1=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=−1

2. Apply the quadratic formula which is given by x=(−b±√(,b2−4*a*c))/(2*a)

x=(−6±√(,6−4*(1)*(−1)))/(2*(1))

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

x=(−6±√(,36+4))/2

x=(−6±√(,40))/2

4. Simplify the radical by factoring out the largest perfect square from √(,40)

√(,40)=√(,4⋅10)=2√(,10)

x=(−6±2√(,10))/2

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

x=−3±√(,10)

Final Answer

x=−3±√(,10)

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