Solve frac{-4+sqrt{4^2-4(1)(-6)}}{2(1)}

$$\frac{ -4+ \sqrt{ { 4 }^{ 2 } -4(1)(-6) } }{ 2(1) }$$

Evaluate

$$\sqrt{10}-2\approx 1.16227766$$

Solution Steps

Calculate 4 to the power of 2 and get 16.

$$\frac{-4+\sqrt{16-4\times 1\left(-6\right)}}{2\times 1}$$

Multiply 4 and 1 to get 4.

$$\frac{-4+\sqrt{16-4\left(-6\right)}}{2\times 1}$$

Multiply 4 and -6 to get -24.

$$\frac{-4+\sqrt{16-\left(-24\right)}}{2\times 1}$$

The opposite of -24 is 24.

$$\frac{-4+\sqrt{16+24}}{2\times 1}$$

Add 16 and 24 to get 40.

$$\frac{-4+\sqrt{40}}{2\times 1}$$

Factor 40=2^{2}\times 10. Rewrite the square root of the product \sqrt{2^{2}\times 10} as the product of square roots \sqrt{2^{2}}\sqrt{10}. Take the square root of 2^{2}.

$$\frac{-4+2\sqrt{10}}{2\times 1}$$

Multiply 2 and 1 to get 2.

$$\frac{-4+2\sqrt{10}}{2}$$

Divide each term of -4+2\sqrt{10} by 2 to get -2+\sqrt{10}.

$$-2+\sqrt{10}$$