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

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

Evaluate

$$-4\sqrt{7}\approx -10.583005244$$

Solution Steps

Calculate 4 to the power of 2 and get 16.

$$\frac{-4\sqrt{16-4\left(-3\right)}}{2}$$

Multiply 4 and -3 to get -12.

$$\frac{-4\sqrt{16-\left(-12\right)}}{2}$$

The opposite of -12 is 12.

$$\frac{-4\sqrt{16+12}}{2}$$

Add 16 and 12 to get 28.

$$\frac{-4\sqrt{28}}{2}$$

Factor 28=2^{2}\times 7. Rewrite the square root of the product \sqrt{2^{2}\times 7} as the product of square roots \sqrt{2^{2}}\sqrt{7}. Take the square root of 2^{2}.

$$\frac{-4\times 2\sqrt{7}}{2}$$

Multiply -4 and 2 to get -8.

$$\frac{-8\sqrt{7}}{2}$$

Divide -8\sqrt{7} by 2 to get -4\sqrt{7}.

$$-4\sqrt{7}$$