Solve 7x^2-22x-13

Question

7 x^{2} - 22 x - 13

Find the roots

x_{1} = \frac{11 - 2 53}{7}, x_{2} = \frac{11 + 2 53}{7}

Alternative Form

x_{1} \approx - 0.508603, x_{2} \approx 3.65146

Evaluate

7 x^{2} - 22 x - 13

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

7 x^{2} - 22 x - 13 = 0

Substitute a= 7,b= - 22 and c= - 13 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{22 \pm ( - 22 ) ^{2} - 4 \times 7 ( - 13 )}{2 \times 7}

Simplify the expression

x = \frac{22 \pm ( - 22 ) ^{2} - 4 \times 7 ( - 13 )}{14}

Simplify the expression

More Steps

x = \frac{22 \pm 848}{14}

Simplify the radical expression

More Steps

x = \frac{22 \pm 4 53}{14}

Separate the equation into 2 possible cases

x = \frac{22 + 4 53}{14} x = \frac{22 - 4 53}{14}

Simplify the expression

More Steps

x = \frac{11 + 2 53}{7} x = \frac{22 - 4 53}{14}

Simplify the expression

More Steps

x = \frac{11 + 2 53}{7} x = \frac{11 - 2 53}{7}

Solution

x_{1} = \frac{11 - 2 53}{7}, x_{2} = \frac{11 + 2 53}{7}

Alternative Form

x_{1} \approx - 0.508603, x_{2} \approx 3.65146

Show Solution