Solve 15/5.3x-30/3.35sqrt{5^275}x

$$1 \frac{ 5 }{ 5.3 } x- \frac{ 30 }{ 3.35 } \sqrt{ { 5 }^{ 2 } 75 } x$$

Factor

$$\frac{\left(6901-795000\sqrt{3}\right)x}{3551}$$

Solution Steps

Multiply 1 and 5.3 to get 5.3.

$$factor(\frac{5.3+5}{5.3}x-\frac{30}{3.35}\sqrt{5^{2}\times 75}x)$$

Add 5.3 and 5 to get 10.3.

$$factor(\frac{10.3}{5.3}x-\frac{30}{3.35}\sqrt{5^{2}\times 75}x)$$

Expand \frac{10.3}{5.3} by multiplying both numerator and the denominator by 10.

$$factor(\frac{103}{53}x-\frac{30}{3.35}\sqrt{5^{2}\times 75}x)$$

Expand \frac{30}{3.35} by multiplying both numerator and the denominator by 100.

$$factor(\frac{103}{53}x-\frac{3000}{335}\sqrt{5^{2}\times 75}x)$$

Reduce the fraction \frac{3000}{335} to lowest terms by extracting and canceling out 5.

$$factor(\frac{103}{53}x-\frac{600}{67}\sqrt{5^{2}\times 75}x)$$

Calculate 5 to the power of 2 and get 25.

$$factor(\frac{103}{53}x-\frac{600}{67}\sqrt{25\times 75}x)$$

Multiply 25 and 75 to get 1875.

$$factor(\frac{103}{53}x-\frac{600}{67}\sqrt{1875}x)$$

Factor 1875=25^{2}\times 3. Rewrite the square root of the product \sqrt{25^{2}\times 3} as the product of square roots \sqrt{25^{2}}\sqrt{3}. Take the square root of 25^{2}.

$$factor(\frac{103}{53}x-\frac{600}{67}\times 25\sqrt{3}x)$$

Express \frac{600}{67}\times 25 as a single fraction.

$$factor(\frac{103}{53}x-\frac{600\times 25}{67}\sqrt{3}x)$$

Multiply 600 and 25 to get 15000.

$$factor(\frac{103}{53}x-\frac{15000}{67}\sqrt{3}x)$$

Factor out \frac{1}{3551}.

$$\frac{6901x-795000\sqrt{3}x}{3551}$$

Consider 6901x-795000\sqrt{3}x. Factor out x.

$$x\left(6901-795000\sqrt{3}\right)$$

Rewrite the complete factored expression.

$$\frac{x\left(6901-795000\sqrt{3}\right)}{3551}$$

Evaluate

$$-\frac{15000\sqrt{3}x}{67}+\frac{103x}{53}$$