Solve -10*178-(1x-3)/sqrt{10(203)-(1)*sqrt{10(1.59)-(9)}}

$$\frac { - 10 \times 178 - ( 1 x - 3 ) } { \sqrt { 10 ( 203 ) - ( 1 ) } \times \sqrt { 10 ( 1.59 ) - ( 9 ) } }$$

Evaluate

$$-\frac{\sqrt{1400010}\left(x+1777\right)}{140001}$$

Solution Steps

Multiply -10 and 178 to get -1780.

$$\frac{-1780-\left(1x-3\right)}{\sqrt{10\times 203-1}\sqrt{10\times 1.59-9}}$$

Multiply 10 and 203 to get 2030.

$$\frac{-1780-\left(1x-3\right)}{\sqrt{2030-1}\sqrt{10\times 1.59-9}}$$

Subtract 1 from 2030 to get 2029.

$$\frac{-1780-\left(1x-3\right)}{\sqrt{2029}\sqrt{10\times 1.59-9}}$$

Multiply 10 and 1.59 to get 15.9.

$$\frac{-1780-\left(1x-3\right)}{\sqrt{2029}\sqrt{15.9-9}}$$

Subtract 9 from 15.9 to get 6.9.

$$\frac{-1780-\left(1x-3\right)}{\sqrt{2029}\sqrt{6.9}}$$

To multiply \sqrt{2029} and \sqrt{6.9}, multiply the numbers under the square root.

$$\frac{-1780-\left(1x-3\right)}{\sqrt{14000.1}}$$

Rationalize the denominator of \frac{-1780-\left(1x-3\right)}{\sqrt{14000.1}} by multiplying numerator and denominator by \sqrt{14000.1}.

$$\frac{\left(-1780-\left(1x-3\right)\right)\sqrt{14000.1}}{\left(\sqrt{14000.1}\right)^{2}}$$

The square of \sqrt{14000.1} is 14000.1.

$$\frac{\left(-1780-\left(1x-3\right)\right)\sqrt{14000.1}}{14000.1}$$

To find the opposite of 1x-3, find the opposite of each term.

$$\frac{\left(-1780-x-\left(-3\right)\right)\sqrt{14000.1}}{14000.1}$$

The opposite of -3 is 3.

$$\frac{\left(-1780-x+3\right)\sqrt{14000.1}}{14000.1}$$

Add -1780 and 3 to get -1777.

$$\frac{\left(-1777-x\right)\sqrt{14000.1}}{14000.1}$$

Use the distributive property to multiply -1777-x by \sqrt{14000.1}.

$$\frac{-1777\sqrt{14000.1}-x\sqrt{14000.1}}{14000.1}$$

Factor

$$-\frac{\sqrt{1400010}\left(x+1777\right)}{140001}$$