Solve frac{-(4)-sqrt{4^2-4(5)(-33)}}{2(5)}

$$\frac{ -(4)- \sqrt{ { 4 }^{ 2 } -4(5)(-33) } }{ 2(5) }$$

Evaluate

$$-3$$

Solution Steps

Calculate 4 to the power of 2 and get 16.

$$\frac{-4-\sqrt{16-4\times 5\left(-33\right)}}{2\times 5}$$

Multiply 4 and 5 to get 20.

$$\frac{-4-\sqrt{16-20\left(-33\right)}}{2\times 5}$$

Multiply 20 and -33 to get -660.

$$\frac{-4-\sqrt{16-\left(-660\right)}}{2\times 5}$$

The opposite of -660 is 660.

$$\frac{-4-\sqrt{16+660}}{2\times 5}$$

Add 16 and 660 to get 676.

$$\frac{-4-\sqrt{676}}{2\times 5}$$

Calculate the square root of 676 and get 26.

$$\frac{-4-26}{2\times 5}$$

Subtract 26 from -4 to get -30.

$$\frac{-30}{2\times 5}$$

Multiply 2 and 5 to get 10.

$$\frac{-30}{10}$$

Divide -30 by 10 to get -3.

$$-3$$

Factor

$$-3$$