Solve -9+sqrt{9^2-4*2*18}

$$-9+ \sqrt{ { 9 }^{ 2 } -4 \cdot 2 \cdot 18 }$$

Evaluate (complex solution)

$$-9+3\sqrt{7}i\approx -9+7.937253933i$$

Solution Steps

Calculate 9 to the power of 2 and get 81.

$$-9+\sqrt{81-4\times 2\times 18}$$

Multiply 4 and 2 to get 8.

$$-9+\sqrt{81-8\times 18}$$

Multiply 8 and 18 to get 144.

$$-9+\sqrt{81-144}$$

Subtract 144 from 81 to get -63.

$$-9+\sqrt{-63}$$

Factor -63=\left(3i\right)^{2}\times 7. Rewrite the square root of the product \sqrt{\left(3i\right)^{2}\times 7} as the product of square roots \sqrt{\left(3i\right)^{2}}\sqrt{7}. Take the square root of \left(3i\right)^{2}.

$$-9+3i\sqrt{7}$$

Factor (complex solution)

$$-9+3\sqrt{7}i$$

Evaluate

$$\text{Indeterminate}$$