Solve \[11x^2-6x-2=0\]

Evaluate

11 x^{2} - 6 x - 2 = 0

Substitute a= 11,b= - 6 and c= - 2 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{6 \pm ( - 6 ) ^{2} - 4 \times 11 ( - 2 )}{2 \times 11}

Simplify the expression

x = \frac{6 \pm ( - 6 ) ^{2} - 4 \times 11 ( - 2 )}{22}

Simplify the expression

More Steps

x = \frac{6 \pm 124}{22}

Simplify the radical expression

More Steps

x = \frac{6 \pm 2 31}{22}

Separate the equation into 2 possible cases

x = \frac{6 + 2 31}{22} x = \frac{6 - 2 31}{22}

Simplify the expression

More Steps

x = \frac{3 + 31}{11} x = \frac{6 - 2 31}{22}

Simplify the expression

More Steps

x = \frac{3 + 31}{11} x = \frac{3 - 31}{11}

Solution

x_{1} = \frac{3 - 31}{11}, x_{2} = \frac{3 + 31}{11}

Alternative Form

x_{1} \approx - 0.233433, x_{2} \approx 0.778888

Solve the quadratic equation