Solve 11x^2-196x-135

Question

Find the roots

x_{1} = \frac{98 - 11089}{11}, x_{2} = \frac{98 + 11089}{11}

Alternative Form

x_{1} \approx - 0.664029, x_{2} \approx 18.482211

Evaluate

11 x^{2} - 196 x - 135

To find the roots of the expression,set the expression equal to 0

11 x^{2} - 196 x - 135 = 0

Substitute a= 11,b= - 196 and c= - 135 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{196 \pm ( - 196 ) ^{2} - 4 \times 11 ( - 135 )}{2 \times 11}

Simplify the expression

x = \frac{196 \pm ( - 196 ) ^{2} - 4 \times 11 ( - 135 )}{22}

Simplify the expression

More Steps

x = \frac{196 \pm 44356}{22}

Simplify the radical expression

More Steps

x = \frac{196 \pm 2 11089}{22}

Separate the equation into 2 possible cases

x = \frac{196 + 2 11089}{22} x = \frac{196 - 2 11089}{22}

Simplify the expression

More Steps

x = \frac{98 + 11089}{11} x = \frac{196 - 2 11089}{22}

Simplify the expression

More Steps

x = \frac{98 + 11089}{11} x = \frac{98 - 11089}{11}

Solution

x_{1} = \frac{98 - 11089}{11}, x_{2} = \frac{98 + 11089}{11}

Alternative Form

x_{1} \approx - 0.664029, x_{2} \approx 18.482211

Show Solution