Solve frac{130-sqrt{130^2-4*5*25}}{-10}

$$\frac { 130 - \sqrt { 130 ^ { 2 } - 4 \times 5 \times 25 } } { - 10 }$$

Evaluate

$$2\sqrt{41}-13\approx -0.193751525$$

Solution Steps

Calculate 130 to the power of 2 and get 16900.

$$\frac{130-\sqrt{16900-4\times 5\times 25}}{-10}$$

Multiply 4 and 5 to get 20.

$$\frac{130-\sqrt{16900-20\times 25}}{-10}$$

Multiply 20 and 25 to get 500.

$$\frac{130-\sqrt{16900-500}}{-10}$$

Subtract 500 from 16900 to get 16400.

$$\frac{130-\sqrt{16400}}{-10}$$

Factor 16400=20^{2}\times 41. Rewrite the square root of the product \sqrt{20^{2}\times 41} as the product of square roots \sqrt{20^{2}}\sqrt{41}. Take the square root of 20^{2}.

$$\frac{130-20\sqrt{41}}{-10}$$

Divide each term of 130-20\sqrt{41} by -10 to get -13+2\sqrt{41}.

$$-13+2\sqrt{41}$$

Factor

$$2 \sqrt{41} - 13 = -0.193751525$$