Solve frac{-60+sqrt{60^2-4*4*-224}}{2*4}

$$\frac{ -60+ \sqrt{ { 60 }^{ 2 } -4 \times 4 \times -224 } }{ 2 \times 4 }$$

Evaluate

$$\frac{\sqrt{449}-15}{2}\approx 3.09481005$$

Solution Steps

Calculate 60 to the power of 2 and get 3600.

$$\frac{-60+\sqrt{3600-4\times 4\left(-224\right)}}{2\times 4}$$

Multiply 4 and 4 to get 16.

$$\frac{-60+\sqrt{3600-16\left(-224\right)}}{2\times 4}$$

Multiply 16 and -224 to get -3584.

$$\frac{-60+\sqrt{3600-\left(-3584\right)}}{2\times 4}$$

The opposite of -3584 is 3584.

$$\frac{-60+\sqrt{3600+3584}}{2\times 4}$$

Add 3600 and 3584 to get 7184.

$$\frac{-60+\sqrt{7184}}{2\times 4}$$

Factor 7184=4^{2}\times 449. Rewrite the square root of the product \sqrt{4^{2}\times 449} as the product of square roots \sqrt{4^{2}}\sqrt{449}. Take the square root of 4^{2}.

$$\frac{-60+4\sqrt{449}}{2\times 4}$$

Multiply 2 and 4 to get 8.

$$\frac{-60+4\sqrt{449}}{8}$$

Factor

$$\frac{\sqrt{449} - 15}{2} = 3.0948100502085456$$