Solve 6*sqrt{25}-25/sqrt{sqrt[3]{512}}*56x=y+xz*654

$$6 \times \sqrt{ 25 } - 2 \frac { 5 } { \sqrt{ \sqrt[3]{ 512 } } } \times 56x=y+xz \times 654$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{2}\left(30-y\right)}{2\left(327\sqrt{2}z+140\right)}\text{, }&z\neq -\frac{70\sqrt{2}}{327}\\x\in \mathrm{C}\text{, }&y=30\text{ and }z=-\frac{70\sqrt{2}}{327}\end{matrix}\right.$$

Steps for Solving Linear Equation

Calculate the square root of 25 and get 5.

$$6\times 5-2\times 56\times \frac{5}{\sqrt{\sqrt[3]{512}}}x=y+xz\times 654$$

Multiply 6 and 5 to get 30.

$$30-2\times 56\times \frac{5}{\sqrt{\sqrt[3]{512}}}x=y+xz\times 654$$

Multiply 2 and 56 to get 112.

$$30-112\times \frac{5}{\sqrt{\sqrt[3]{512}}}x=y+xz\times 654$$

Calculate \sqrt[3]{512} and get 8.

$$30-112\times \frac{5}{\sqrt{8}}x=y+xz\times 654$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$30-112\times \frac{5}{2\sqrt{2}}x=y+xz\times 654$$

Rationalize the denominator of \frac{5}{2\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$30-112\times \frac{5\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}x=y+xz\times 654$$

The square of \sqrt{2} is 2.

$$30-112\times \frac{5\sqrt{2}}{2\times 2}x=y+xz\times 654$$

Multiply 2 and 2 to get 4.

$$30-112\times \frac{5\sqrt{2}}{4}x=y+xz\times 654$$

Cancel out 4, the greatest common factor in 112 and 4.

$$30-28\times 5\sqrt{2}x=y+xz\times 654$$

Multiply 28 and 5 to get 140.

$$30-140\sqrt{2}x=y+xz\times 654$$

Subtract xz\times 654 from both sides.

$$30-140\sqrt{2}x-xz\times 654=y$$

Multiply -1 and 654 to get -654.

$$30-140\sqrt{2}x-654xz=y$$

Subtract 30 from both sides.

$$-140\sqrt{2}x-654xz=y-30$$

Combine all terms containing x.

$$\left(-140\sqrt{2}-654z\right)x=y-30$$

The equation is in standard form.

$$\left(-654z-140\sqrt{2}\right)x=y-30$$

Divide both sides by -140\sqrt{2}-654z.

$$\frac{\left(-654z-140\sqrt{2}\right)x}{-654z-140\sqrt{2}}=\frac{y-30}{-654z-140\sqrt{2}}$$

Dividing by -140\sqrt{2}-654z undoes the multiplication by -140\sqrt{2}-654z.

$$x=\frac{y-30}{-654z-140\sqrt{2}}$$

Divide y-30 by -140\sqrt{2}-654z.

$$x=-\frac{y-30}{2\left(327z+70\sqrt{2}\right)}$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{2}\left(30-y\right)}{2\left(327\sqrt{2}z+140\right)}\text{, }&z\neq -\frac{70\sqrt{2}}{327}\\x\in \mathrm{R}\text{, }&y=30\text{ and }z=-\frac{70\sqrt{2}}{327}\end{matrix}\right.$$

Steps for Solving Linear Equation

Calculate the square root of 25 and get 5.

$$6\times 5-2\times 56\times \frac{5}{\sqrt{\sqrt[3]{512}}}x=y+xz\times 654$$

Multiply 6 and 5 to get 30.

$$30-2\times 56\times \frac{5}{\sqrt{\sqrt[3]{512}}}x=y+xz\times 654$$

Multiply 2 and 56 to get 112.

$$30-112\times \frac{5}{\sqrt{\sqrt[3]{512}}}x=y+xz\times 654$$

Calculate \sqrt[3]{512} and get 8.

$$30-112\times \frac{5}{\sqrt{8}}x=y+xz\times 654$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$30-112\times \frac{5}{2\sqrt{2}}x=y+xz\times 654$$

Rationalize the denominator of \frac{5}{2\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$30-112\times \frac{5\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}x=y+xz\times 654$$

The square of \sqrt{2} is 2.

$$30-112\times \frac{5\sqrt{2}}{2\times 2}x=y+xz\times 654$$

Multiply 2 and 2 to get 4.

$$30-112\times \frac{5\sqrt{2}}{4}x=y+xz\times 654$$

Cancel out 4, the greatest common factor in 112 and 4.

$$30-28\times 5\sqrt{2}x=y+xz\times 654$$

Multiply 28 and 5 to get 140.

$$30-140\sqrt{2}x=y+xz\times 654$$

Subtract xz\times 654 from both sides.

$$30-140\sqrt{2}x-xz\times 654=y$$

Multiply -1 and 654 to get -654.

$$30-140\sqrt{2}x-654xz=y$$

Subtract 30 from both sides.

$$-140\sqrt{2}x-654xz=y-30$$

Combine all terms containing x.

$$\left(-140\sqrt{2}-654z\right)x=y-30$$

The equation is in standard form.

$$\left(-654z-140\sqrt{2}\right)x=y-30$$

Divide both sides by -140\sqrt{2}-654z.

$$\frac{\left(-654z-140\sqrt{2}\right)x}{-654z-140\sqrt{2}}=\frac{y-30}{-654z-140\sqrt{2}}$$

Dividing by -140\sqrt{2}-654z undoes the multiplication by -140\sqrt{2}-654z.

$$x=\frac{y-30}{-654z-140\sqrt{2}}$$

Divide y-30 by -140\sqrt{2}-654z.

$$x=-\frac{y-30}{2\left(327z+70\sqrt{2}\right)}$$

Solve for y

$$y=-654xz-140\sqrt{2}x+30$$