Solve frac{0-sqrt{2^2-4*2*-15}}{2*2}

$$\frac{ 0- \sqrt{ { 2 }^{ 2 } -4 \times 2 \times -15 } }{ 2 \times 2 }$$

Evaluate

$$-\frac{\sqrt{31}}{2}\approx -2.783882181$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

$$\frac{0-\sqrt{4-4\times 2\left(-15\right)}}{2\times 2}$$

Multiply 4 and 2 to get 8.

$$\frac{0-\sqrt{4-8\left(-15\right)}}{2\times 2}$$

Multiply 8 and -15 to get -120.

$$\frac{0-\sqrt{4-\left(-120\right)}}{2\times 2}$$

The opposite of -120 is 120.

$$\frac{0-\sqrt{4+120}}{2\times 2}$$

Add 4 and 120 to get 124.

$$\frac{0-\sqrt{124}}{2\times 2}$$

Factor 124=2^{2}\times 31. Rewrite the square root of the product \sqrt{2^{2}\times 31} as the product of square roots \sqrt{2^{2}}\sqrt{31}. Take the square root of 2^{2}.

$$\frac{0-2\sqrt{31}}{2\times 2}$$

Anything plus zero gives itself.

$$\frac{-2\sqrt{31}}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$\frac{-2\sqrt{31}}{4}$$

Divide -2\sqrt{31} by 4 to get -\frac{1}{2}\sqrt{31}.

$$-\frac{1}{2}\sqrt{31}$$