Solve x^0=frac{30+4^2+sqrt{8}1+5^2x5}{4x+15+2(6-5)}

$$x ^ { 0 } = \frac { 30 + 4 ^ { 2 } + \sqrt { 8 } 1 + 5 ^ { 2 } x 5 } { 4 x + 15 + 2 ( 6 - 5 ) }$$

Solve for x_5

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

$$x\neq 0\text{ and }x\neq -\frac{17}{4}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 4x+17.

$$\left(4x+17\right)x^{0}=30+4^{2}+1\sqrt{8}+5^{2}x_{5}$$

Use the distributive property to multiply 4x+17 by x^{0}.

$$4xx^{0}+17x^{0}=30+4^{2}+1\sqrt{8}+5^{2}x_{5}$$

To multiply powers of the same base, add their exponents. Add 1 and 0 to get 1.

$$4x^{1}+17x^{0}=30+4^{2}+1\sqrt{8}+5^{2}x_{5}$$

Calculate x to the power of 1 and get x.

$$4x+17x^{0}=30+4^{2}+1\sqrt{8}+5^{2}x_{5}$$

Calculate 4 to the power of 2 and get 16.

$$4x+17x^{0}=30+16+1\sqrt{8}+5^{2}x_{5}$$

Add 30 and 16 to get 46.

$$4x+17x^{0}=46+1\sqrt{8}+5^{2}x_{5}$$

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}.

$$4x+17x^{0}=46+1\times 2\sqrt{2}+5^{2}x_{5}$$

Multiply 1 and 2 to get 2.

$$4x+17x^{0}=46+2\sqrt{2}+5^{2}x_{5}$$

Calculate 5 to the power of 2 and get 25.

$$4x+17x^{0}=46+2\sqrt{2}+25x_{5}$$

Swap sides so that all variable terms are on the left hand side.

$$46+2\sqrt{2}+25x_{5}=4x+17x^{0}$$

Subtract 46 from both sides.

$$2\sqrt{2}+25x_{5}=4x+17x^{0}-46$$

Subtract 2\sqrt{2} from both sides.

$$25x_{5}=4x+17x^{0}-46-2\sqrt{2}$$

The equation is in standard form.

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

Divide both sides by 25.

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

Dividing by 25 undoes the multiplication by 25.

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

Solve for x (complex solution)

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

$$x_{5}\neq \frac{-2\sqrt{2}-29}{25}\text{ and }x_{5}\neq \frac{-2\sqrt{2}-46}{25}\text{ and }x_{5}\neq \frac{-2\sqrt{2}-29}{25}$$

Solve for x

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

$$x_{5}\neq \frac{-2\sqrt{2}-29}{25}\text{ and }x_{5}\neq \frac{-2\sqrt{2}-46}{25}$$