Solve frac{-12-sqrt{12^2-4-02*7}}{2-02}

$$\frac{ -12- \sqrt{ { 12 }^{ 2 } -4-02 \cdot 7 } }{ 2-02 }$$

Evaluate

$$-\sqrt{35}-6\approx -11.916079783$$

Solution Steps

Calculate 12 to the power of 2 and get 144.

$$\frac{-12-\sqrt{144-4-0\times 2\times 7}}{2-0\times 2}$$

Subtract 4 from 144 to get 140.

$$\frac{-12-\sqrt{140-0\times 2\times 7}}{2-0\times 2}$$

Multiply 0 and 2 to get 0.

$$\frac{-12-\sqrt{140-0\times 7}}{2-0\times 2}$$

Multiply 0 and 7 to get 0.

$$\frac{-12-\sqrt{140-0}}{2-0\times 2}$$

Subtract 0 from 140 to get 140.

$$\frac{-12-\sqrt{140}}{2-0\times 2}$$

Factor 140=2^{2}\times 35. Rewrite the square root of the product \sqrt{2^{2}\times 35} as the product of square roots \sqrt{2^{2}}\sqrt{35}. Take the square root of 2^{2}.

$$\frac{-12-2\sqrt{35}}{2-0\times 2}$$

Multiply 0 and 2 to get 0.

$$\frac{-12-2\sqrt{35}}{2-0}$$

Subtract 0 from 2 to get 2.

$$\frac{-12-2\sqrt{35}}{2}$$

Divide each term of -12-2\sqrt{35} by 2 to get -6-\sqrt{35}.

$$-6-\sqrt{35}$$

Factor

$$-\sqrt{35}-6$$