Solve frac{-1+sqrt{1^2-4*-9*8}}{2*-9}

$$\frac{ -1+ \sqrt{ { 1 }^{ 2 } -4 \times -9 \times 8 } }{ 2 \times -9 }$$

Evaluate

$$-\frac{8}{9}\approx -0.888888889$$

Solution Steps

Calculate 1 to the power of 2 and get 1.

$$\frac{-1+\sqrt{1-4\left(-9\right)\times 8}}{2\left(-9\right)}$$

Multiply 4 and -9 to get -36.

$$\frac{-1+\sqrt{1-\left(-36\times 8\right)}}{2\left(-9\right)}$$

Multiply -36 and 8 to get -288.

$$\frac{-1+\sqrt{1-\left(-288\right)}}{2\left(-9\right)}$$

The opposite of -288 is 288.

$$\frac{-1+\sqrt{1+288}}{2\left(-9\right)}$$

Add 1 and 288 to get 289.

$$\frac{-1+\sqrt{289}}{2\left(-9\right)}$$

Calculate the square root of 289 and get 17.

$$\frac{-1+17}{2\left(-9\right)}$$

Add -1 and 17 to get 16.

$$\frac{16}{2\left(-9\right)}$$

Multiply 2 and -9 to get -18.

$$\frac{16}{-18}$$

Reduce the fraction \frac{16}{-18} to lowest terms by extracting and canceling out 2.

$$-\frac{8}{9}$$

Factor

$$-\frac{8}{9} = -0.8888888888888888$$