Solve frac{10+sqrt{100-4*(-29)}}{2}

$$\frac { 10 + \sqrt { 100 - 4 \cdot ( - 29 ) } } { 2 }$$

Evaluate

$$3\sqrt{6}+5\approx 12.348469228$$

Solution Steps

Multiply 4 and -29 to get -116.

$$\frac{10+\sqrt{100-\left(-116\right)}}{2}$$

The opposite of -116 is 116.

$$\frac{10+\sqrt{100+116}}{2}$$

Add 100 and 116 to get 216.

$$\frac{10+\sqrt{216}}{2}$$

Factor 216=6^{2}\times 6. Rewrite the square root of the product \sqrt{6^{2}\times 6} as the product of square roots \sqrt{6^{2}}\sqrt{6}. Take the square root of 6^{2}.

$$\frac{10+6\sqrt{6}}{2}$$

Divide each term of 10+6\sqrt{6} by 2 to get 5+3\sqrt{6}.

$$5+3\sqrt{6}$$

Factor

$$3 \sqrt{6} + 5 = 12.348469228$$