Solve frac{-(-14)+sqrt{14^2-4(2)(6)}}{2(2)}

$$\frac{ -(-14)+ \sqrt{ { 14 }^{ 2 } -4(2)(6) } }{ 2(2) }$$

Evaluate

$$\frac{\sqrt{37}+7}{2}\approx 6.541381265$$

Solution Steps

The opposite of -14 is 14.

$$\frac{14+\sqrt{14^{2}-4\times 2\times 6}}{2\times 2}$$

Calculate 14 to the power of 2 and get 196.

$$\frac{14+\sqrt{196-4\times 2\times 6}}{2\times 2}$$

Multiply 4 and 2 to get 8.

$$\frac{14+\sqrt{196-8\times 6}}{2\times 2}$$

Multiply 8 and 6 to get 48.

$$\frac{14+\sqrt{196-48}}{2\times 2}$$

Subtract 48 from 196 to get 148.

$$\frac{14+\sqrt{148}}{2\times 2}$$

Factor 148=2^{2}\times 37. Rewrite the square root of the product \sqrt{2^{2}\times 37} as the product of square roots \sqrt{2^{2}}\sqrt{37}. Take the square root of 2^{2}.

$$\frac{14+2\sqrt{37}}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$\frac{14+2\sqrt{37}}{4}$$

Factor

$$\frac{\sqrt{37} + 7}{2} = 6.541381265149109$$