Solve frac{-5+sqrt{5^2+4*2*1050}}{2*2}+frac{-5-sqrt{5^2+4*2*1050}}{2*2}

$$\frac{ -5+ \sqrt{ { 5 }^{ 2 } +4 \cdot 2 \cdot 1050 } }{ 2 \times 2 } + \frac{ -5- \sqrt{ { 5 }^{ 2 } +4 \cdot 2 \cdot 1050 } }{ 2 \times 2 }$$

Evaluate

$$-\frac{5}{2}=-2.5$$

Short Solution Steps

Calculate 5 to the power of 2 and get 25.

$$\frac{-5+\sqrt{25+4\times 2\times 1050}}{2\times 2}+\frac{-5-\sqrt{5^{2}+4\times 2\times 1050}}{2\times 2}$$

Multiply 4 and 2 to get 8.

$$\frac{-5+\sqrt{25+8\times 1050}}{2\times 2}+\frac{-5-\sqrt{5^{2}+4\times 2\times 1050}}{2\times 2}$$

Multiply 8 and 1050 to get 8400.

$$\frac{-5+\sqrt{25+8400}}{2\times 2}+\frac{-5-\sqrt{5^{2}+4\times 2\times 1050}}{2\times 2}$$

Add 25 and 8400 to get 8425.

$$\frac{-5+\sqrt{8425}}{2\times 2}+\frac{-5-\sqrt{5^{2}+4\times 2\times 1050}}{2\times 2}$$

Factor 8425=5^{2}\times 337. Rewrite the square root of the product \sqrt{5^{2}\times 337} as the product of square roots \sqrt{5^{2}}\sqrt{337}. Take the square root of 5^{2}.

$$\frac{-5+5\sqrt{337}}{2\times 2}+\frac{-5-\sqrt{5^{2}+4\times 2\times 1050}}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$\frac{-5+5\sqrt{337}}{4}+\frac{-5-\sqrt{5^{2}+4\times 2\times 1050}}{2\times 2}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{-5+5\sqrt{337}}{4}+\frac{-5-\sqrt{25+4\times 2\times 1050}}{2\times 2}$$

Multiply 4 and 2 to get 8.

$$\frac{-5+5\sqrt{337}}{4}+\frac{-5-\sqrt{25+8\times 1050}}{2\times 2}$$

Multiply 8 and 1050 to get 8400.

$$\frac{-5+5\sqrt{337}}{4}+\frac{-5-\sqrt{25+8400}}{2\times 2}$$

Add 25 and 8400 to get 8425.

$$\frac{-5+5\sqrt{337}}{4}+\frac{-5-\sqrt{8425}}{2\times 2}$$

Factor 8425=5^{2}\times 337. Rewrite the square root of the product \sqrt{5^{2}\times 337} as the product of square roots \sqrt{5^{2}}\sqrt{337}. Take the square root of 5^{2}.

$$\frac{-5+5\sqrt{337}}{4}+\frac{-5-5\sqrt{337}}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$\frac{-5+5\sqrt{337}}{4}+\frac{-5-5\sqrt{337}}{4}$$

Since \frac{-5+5\sqrt{337}}{4} and \frac{-5-5\sqrt{337}}{4} have the same denominator, add them by adding their numerators.

$$\frac{-5+5\sqrt{337}-5-5\sqrt{337}}{4}$$

Do the calculations in -5+5\sqrt{337}-5-5\sqrt{337}.

$$\frac{-10}{4}$$

Reduce the fraction \frac{-10}{4} to lowest terms by extracting and canceling out 2.

$$-\frac{5}{2}$$

Factor

$$-\frac{5}{2} = -2\frac{1}{2} = -2.5$$