Solve sqrt{2}(2x+3)-4=xsqrt{2}(1-2sqrt{2})

$$\sqrt { 2 } ( 2 x + 3 ) - 4 = x \sqrt { 2 } ( 1 - 2 \sqrt { 2 } )$$

Solve for x

$$x=\frac{11-8\sqrt{2}}{7}\approx -0.0448155$$

Steps for Solving Linear Equation

Use the distributive property to multiply \sqrt{2} by 2x+3.

$$2\sqrt{2}x+3\sqrt{2}-4=x\sqrt{2}\left(1-2\sqrt{2}\right)$$

Use the distributive property to multiply x\sqrt{2} by 1-2\sqrt{2}.

$$2\sqrt{2}x+3\sqrt{2}-4=x\sqrt{2}-2x\left(\sqrt{2}\right)^{2}$$

The square of \sqrt{2} is 2.

$$2\sqrt{2}x+3\sqrt{2}-4=x\sqrt{2}-2x\times 2$$

Multiply -2 and 2 to get -4.

$$2\sqrt{2}x+3\sqrt{2}-4=x\sqrt{2}-4x$$

Subtract x\sqrt{2} from both sides.

$$2\sqrt{2}x+3\sqrt{2}-4-x\sqrt{2}=-4x$$

Combine 2\sqrt{2}x and -x\sqrt{2} to get \sqrt{2}x.

$$\sqrt{2}x+3\sqrt{2}-4=-4x$$

Add 4x to both sides.

$$\sqrt{2}x+3\sqrt{2}-4+4x=0$$

Subtract 3\sqrt{2} from both sides. Anything subtracted from zero gives its negation.

$$\sqrt{2}x-4+4x=-3\sqrt{2}$$

Add 4 to both sides.

$$\sqrt{2}x+4x=-3\sqrt{2}+4$$

Combine all terms containing x.

$$\left(\sqrt{2}+4\right)x=-3\sqrt{2}+4$$

The equation is in standard form.

$$\left(\sqrt{2}+4\right)x=4-3\sqrt{2}$$

Divide both sides by \sqrt{2}+4.

$$\frac{\left(\sqrt{2}+4\right)x}{\sqrt{2}+4}=\frac{4-3\sqrt{2}}{\sqrt{2}+4}$$

Dividing by \sqrt{2}+4 undoes the multiplication by \sqrt{2}+4.

$$x=\frac{4-3\sqrt{2}}{\sqrt{2}+4}$$

Divide -3\sqrt{2}+4 by \sqrt{2}+4.

$$x=\frac{11-8\sqrt{2}}{7}$$