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

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

Evaluate

$$\sqrt{5}+2\approx 4.236067977$$

Solution Steps

The opposite of -4 is 4.

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

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

$$\frac{4+\sqrt{16-4\times 1\left(-1\right)}}{2\times 1}$$

Multiply 4 and 1 to get 4.

$$\frac{4+\sqrt{16-4\left(-1\right)}}{2\times 1}$$

Multiply 4 and -1 to get -4.

$$\frac{4+\sqrt{16-\left(-4\right)}}{2\times 1}$$

The opposite of -4 is 4.

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

Add 16 and 4 to get 20.

$$\frac{4+\sqrt{20}}{2\times 1}$$

Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.

$$\frac{4+2\sqrt{5}}{2\times 1}$$

Multiply 2 and 1 to get 2.

$$\frac{4+2\sqrt{5}}{2}$$

Divide each term of 4+2\sqrt{5} by 2 to get 2+\sqrt{5}.

$$2+\sqrt{5}$$

Factor

$$\sqrt{5} + 2 = 4.236067977$$