Solve x=50/10-5sqrt{29}

$$x= \frac{ 50 }{ 10-5 \sqrt{ 29 } }$$

Solve for x

$$x=\frac{-2\sqrt{29}-4}{5}\approx -2.954065923$$

Steps for Solving Linear Equation

Rationalize the denominator of \frac{50}{10-5\sqrt{29}} by multiplying numerator and denominator by 10+5\sqrt{29}.

$$x=\frac{50\left(10+5\sqrt{29}\right)}{\left(10-5\sqrt{29}\right)\left(10+5\sqrt{29}\right)}$$

Consider \left(10-5\sqrt{29}\right)\left(10+5\sqrt{29}\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$x=\frac{50\left(10+5\sqrt{29}\right)}{10^{2}-\left(-5\sqrt{29}\right)^{2}}$$

Calculate 10 to the power of 2 and get 100.

$$x=\frac{50\left(10+5\sqrt{29}\right)}{100-\left(-5\sqrt{29}\right)^{2}}$$

Expand \left(-5\sqrt{29}\right)^{2}.

$$x=\frac{50\left(10+5\sqrt{29}\right)}{100-\left(-5\right)^{2}\left(\sqrt{29}\right)^{2}}$$

Calculate -5 to the power of 2 and get 25.

$$x=\frac{50\left(10+5\sqrt{29}\right)}{100-25\left(\sqrt{29}\right)^{2}}$$

The square of \sqrt{29} is 29.

$$x=\frac{50\left(10+5\sqrt{29}\right)}{100-25\times 29}$$

Multiply 25 and 29 to get 725.

$$x=\frac{50\left(10+5\sqrt{29}\right)}{100-725}$$

Subtract 725 from 100 to get -625.

$$x=\frac{50\left(10+5\sqrt{29}\right)}{-625}$$

Divide 50\left(10+5\sqrt{29}\right) by -625 to get -\frac{2}{25}\left(10+5\sqrt{29}\right).

$$x=-\frac{2}{25}\left(10+5\sqrt{29}\right)$$

Use the distributive property to multiply -\frac{2}{25} by 10+5\sqrt{29}.

$$x=-\frac{2}{25}\times 10-\frac{2}{25}\times 5\sqrt{29}$$

Express -\frac{2}{25}\times 10 as a single fraction.

$$x=\frac{-2\times 10}{25}-\frac{2}{25}\times 5\sqrt{29}$$

Multiply -2 and 10 to get -20.

$$x=\frac{-20}{25}-\frac{2}{25}\times 5\sqrt{29}$$

Reduce the fraction \frac{-20}{25} to lowest terms by extracting and canceling out 5.

$$x=-\frac{4}{5}-\frac{2}{25}\times 5\sqrt{29}$$

Express -\frac{2}{25}\times 5 as a single fraction.

$$x=-\frac{4}{5}+\frac{-2\times 5}{25}\sqrt{29}$$

Multiply -2 and 5 to get -10.

$$x=-\frac{4}{5}+\frac{-10}{25}\sqrt{29}$$

Reduce the fraction \frac{-10}{25} to lowest terms by extracting and canceling out 5.

$$x=-\frac{4}{5}-\frac{2}{5}\sqrt{29}$$

Assign x

$$x≔\frac{-2\sqrt{29}-4}{5}$$