Solve frac{-145-sqrt{145^2-4-49*199}}{-98}

$$\frac{ -145- \sqrt{ { 145 }^{ 2 } -4-49 \cdot 199 } }{ -98 }$$

Evaluate

$$\frac{\sqrt{230}}{14}+\frac{145}{98}\approx 2.562859757$$

Solution Steps

Calculate 145 to the power of 2 and get 21025.

$$\frac{-145-\sqrt{21025-4-49\times 199}}{-98}$$

Subtract 4 from 21025 to get 21021.

$$\frac{-145-\sqrt{21021-49\times 199}}{-98}$$

Multiply 49 and 199 to get 9751.

$$\frac{-145-\sqrt{21021-9751}}{-98}$$

Subtract 9751 from 21021 to get 11270.

$$\frac{-145-\sqrt{11270}}{-98}$$

Factor 11270=7^{2}\times 230. Rewrite the square root of the product \sqrt{7^{2}\times 230} as the product of square roots \sqrt{7^{2}}\sqrt{230}. Take the square root of 7^{2}.

$$\frac{-145-7\sqrt{230}}{-98}$$

Multiply both numerator and denominator by -1.

$$\frac{145+7\sqrt{230}}{98}$$