Solve frac{10-sqrt{-10^2-4*3*3}}{2*3}

$$\frac{ 10- \sqrt{ - { 10 }^{ 2 } -4 \times 3 \times 3 } }{ 2 \times 3 }$$

Evaluate (complex solution)

$$\frac{-\sqrt{34}i+5}{3}\approx 1.666666667-1.943650632i$$

Solution Steps

Calculate 10 to the power of 2 and get 100.

$$\frac{10-\sqrt{-100-4\times 3\times 3}}{2\times 3}$$

Multiply 4 and 3 to get 12.

$$\frac{10-\sqrt{-100-12\times 3}}{2\times 3}$$

Multiply 12 and 3 to get 36.

$$\frac{10-\sqrt{-100-36}}{2\times 3}$$

Subtract 36 from -100 to get -136.

$$\frac{10-\sqrt{-136}}{2\times 3}$$

Factor -136=\left(2i\right)^{2}\times 34. Rewrite the square root of the product \sqrt{\left(2i\right)^{2}\times 34} as the product of square roots \sqrt{\left(2i\right)^{2}}\sqrt{34}. Take the square root of \left(2i\right)^{2}.

$$\frac{10-2i\sqrt{34}}{2\times 3}$$

Multiply 2 and 3 to get 6.

$$\frac{10-2i\sqrt{34}}{6}$$

Factor (complex solution)

$$\frac{-\sqrt{34}i+5}{3}$$

Evaluate

$$\text{Indeterminate}$$