Solve frac{-(-1)+sqrt{(-1)^2-12*2*(-1)}}{2*(-1)}

$$\frac { - ( - 1 ) + \sqrt { ( - 1 ) ^ { 2 } - 12 \cdot 2 \cdot ( - 1 ) } } { 2 \cdot ( - 1 ) }$$

Evaluate

$$-3$$

Solution Steps

The opposite of -1 is 1.

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

Calculate -1 to the power of 2 and get 1.

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

Multiply 12 and 2 to get 24.

$$\frac{1+\sqrt{1-24\left(-1\right)}}{2\left(-1\right)}$$

Multiply 24 and -1 to get -24.

$$\frac{1+\sqrt{1-\left(-24\right)}}{2\left(-1\right)}$$

The opposite of -24 is 24.

$$\frac{1+\sqrt{1+24}}{2\left(-1\right)}$$

Add 1 and 24 to get 25.

$$\frac{1+\sqrt{25}}{2\left(-1\right)}$$

Calculate the square root of 25 and get 5.

$$\frac{1+5}{2\left(-1\right)}$$

Add 1 and 5 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

$$-3$$