Solve frac{-(-2)+sqrt{(-2)^2-4(-1)(3)}}{2(-1)}

$$\frac { - ( - 2 ) + \sqrt { ( - 2 ) ^ { 2 } - 4 ( - 1 ) ( 3 ) } } { 2 ( - 1 ) }$$

Evaluate

$$-3$$

Solution Steps

The opposite of -2 is 2.

$$\frac{2+\sqrt{\left(-2\right)^{2}-4\left(-1\right)\times 3}}{2\left(-1\right)}$$

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

$$\frac{2+\sqrt{4-4\left(-1\right)\times 3}}{2\left(-1\right)}$$

Multiply 4 and -1 to get -4.

$$\frac{2+\sqrt{4-\left(-4\times 3\right)}}{2\left(-1\right)}$$

Multiply -4 and 3 to get -12.

$$\frac{2+\sqrt{4-\left(-12\right)}}{2\left(-1\right)}$$

The opposite of -12 is 12.

$$\frac{2+\sqrt{4+12}}{2\left(-1\right)}$$

Add 4 and 12 to get 16.

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

Calculate the square root of 16 and get 4.

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

Add 2 and 4 to get 6.

$$\frac{6}{2\left(-1\right)}$$

Multiply 2 and -1 to get -2.

$$\frac{6}{-2}$$

Divide 6 by -2 to get -3.

$$-3$$

Factor

$$-3$$