Solve frac{-12+-sqrt{12^2-4(1)(-32)}}{2(1)}

$$\frac{ -12+- \sqrt{ { 12 }^{ 2 } -4(1)(-32) } }{ 2(1) }$$

Evaluate

$$-2\sqrt{17}-6\approx -14.246211251$$

Solution Steps

Calculate 12 to the power of 2 and get 144.

$$\frac{-12-\sqrt{144-4\times 1\left(-32\right)}}{2\times 1}$$

Multiply 4 and 1 to get 4.

$$\frac{-12-\sqrt{144-4\left(-32\right)}}{2\times 1}$$

Multiply 4 and -32 to get -128.

$$\frac{-12-\sqrt{144-\left(-128\right)}}{2\times 1}$$

The opposite of -128 is 128.

$$\frac{-12-\sqrt{144+128}}{2\times 1}$$

Add 144 and 128 to get 272.

$$\frac{-12-\sqrt{272}}{2\times 1}$$

Factor 272=4^{2}\times 17. Rewrite the square root of the product \sqrt{4^{2}\times 17} as the product of square roots \sqrt{4^{2}}\sqrt{17}. Take the square root of 4^{2}.

$$\frac{-12-4\sqrt{17}}{2\times 1}$$

Multiply 2 and 1 to get 2.

$$\frac{-12-4\sqrt{17}}{2}$$

Factor

$$2 {(-\sqrt{17} - 3)} = -14.246211251$$