Solve frac{10+sqrt{10^2-4(1)(6)}}{2}

$$\frac{ 10+ \sqrt{ { 10 }^{ 2 } -4(1)(6) } }{ 2 }$$

Evaluate

$$\sqrt{19}+5\approx 9.358898944$$

Solution Steps

Calculate 10 to the power of 2 and get 100.

$$\frac{10+\sqrt{100-4\times 1\times 6}}{2}$$

Multiply 4 and 1 to get 4.

$$\frac{10+\sqrt{100-4\times 6}}{2}$$

Multiply 4 and 6 to get 24.

$$\frac{10+\sqrt{100-24}}{2}$$

Subtract 24 from 100 to get 76.

$$\frac{10+\sqrt{76}}{2}$$

Factor 76=2^{2}\times 19. Rewrite the square root of the product \sqrt{2^{2}\times 19} as the product of square roots \sqrt{2^{2}}\sqrt{19}. Take the square root of 2^{2}.

$$\frac{10+2\sqrt{19}}{2}$$

Divide each term of 10+2\sqrt{19} by 2 to get 5+\sqrt{19}.

$$5+\sqrt{19}$$

Factor

$$\sqrt{19} + 5 = 9.358898944$$