Solve frac{-(-4)+sqrt{-4^2-4*(2)*(1)}}{2*(2)}

$$\frac{ -(-4)+ \sqrt{ { -4 }^{ 2 } -4 \cdot (2) \cdot (1) } }{ 2 \cdot (2) }$$

Evaluate

$$\frac{\sqrt{2}}{2}+1\approx 1.707106781$$

Solution Steps

The opposite of -4 is 4.

$$\frac{4+\sqrt{\left(-4\right)^{2}-4\times 2\times 1}}{2\times 2}$$

Calculate -4 to the power of 2 and get 16.

$$\frac{4+\sqrt{16-4\times 2\times 1}}{2\times 2}$$

Multiply 4 and 2 to get 8.

$$\frac{4+\sqrt{16-8\times 1}}{2\times 2}$$

Multiply 8 and 1 to get 8.

$$\frac{4+\sqrt{16-8}}{2\times 2}$$

Subtract 8 from 16 to get 8.

$$\frac{4+\sqrt{8}}{2\times 2}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$\frac{4+2\sqrt{2}}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$\frac{4+2\sqrt{2}}{4}$$