Solve 2(x+sqrt{2}-sqrt{5})+3=x(sqrt{5}-sqrt{2})

$$2 ( x + \sqrt { 2 } - \sqrt { 5 } ) + 3 = x ( \sqrt { 5 } - \sqrt { 2 } )$$

Solve for x (complex solution)

$$x=\frac{4\sqrt{10}+15\sqrt{5}+40\sqrt{2}-16\sqrt{5}-33\sqrt{2}-56}{31}\approx -1.151208465$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2 by x+\sqrt{2}-\sqrt{5}.

$$2x+2\sqrt{2}-2\sqrt{5}+3=x\left(\sqrt{5}-\sqrt{2}\right)$$

Use the distributive property to multiply x by \sqrt{5}-\sqrt{2}.

$$2x+2\sqrt{2}-2\sqrt{5}+3=x\sqrt{5}-x\sqrt{2}$$

Subtract x\sqrt{5} from both sides.

$$2x+2\sqrt{2}-2\sqrt{5}+3-x\sqrt{5}=-x\sqrt{2}$$

Add x\sqrt{2} to both sides.

$$2x+2\sqrt{2}-2\sqrt{5}+3-x\sqrt{5}+x\sqrt{2}=0$$

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

$$2x-2\sqrt{5}+3-x\sqrt{5}+x\sqrt{2}=-2\sqrt{2}$$

Add 2\sqrt{5} to both sides.

$$2x+3-x\sqrt{5}+x\sqrt{2}=-2\sqrt{2}+2\sqrt{5}$$

Subtract 3 from both sides.

$$2x-x\sqrt{5}+x\sqrt{2}=-2\sqrt{2}+2\sqrt{5}-3$$

Combine all terms containing x.

$$\left(2-\sqrt{5}+\sqrt{2}\right)x=-2\sqrt{2}+2\sqrt{5}-3$$

The equation is in standard form.

$$\left(\sqrt{2}+2-\sqrt{5}\right)x=2\sqrt{5}-2\sqrt{2}-3$$

Divide both sides by 2-\sqrt{5}+\sqrt{2}.

$$\frac{\left(\sqrt{2}+2-\sqrt{5}\right)x}{\sqrt{2}+2-\sqrt{5}}=\frac{2\sqrt{5}-2\sqrt{2}-3}{\sqrt{2}+2-\sqrt{5}}$$

Dividing by 2-\sqrt{5}+\sqrt{2} undoes the multiplication by 2-\sqrt{5}+\sqrt{2}.

$$x=\frac{2\sqrt{5}-2\sqrt{2}-3}{\sqrt{2}+2-\sqrt{5}}$$

Divide -2\sqrt{2}+2\sqrt{5}-3 by 2-\sqrt{5}+\sqrt{2}.

$$x=\frac{4\sqrt{10}+7\sqrt{2}-\sqrt{5}-56}{31}$$

Solve for x

$$x=\frac{4\sqrt{10}+7\sqrt{2}-\sqrt{5}-56}{31}\approx -1.151208465$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2 by x+\sqrt{2}-\sqrt{5}.

$$2x+2\sqrt{2}-2\sqrt{5}+3=x\left(\sqrt{5}-\sqrt{2}\right)$$

Use the distributive property to multiply x by \sqrt{5}-\sqrt{2}.

$$2x+2\sqrt{2}-2\sqrt{5}+3=x\sqrt{5}-x\sqrt{2}$$

Subtract x\sqrt{5} from both sides.

$$2x+2\sqrt{2}-2\sqrt{5}+3-x\sqrt{5}=-x\sqrt{2}$$

Add x\sqrt{2} to both sides.

$$2x+2\sqrt{2}-2\sqrt{5}+3-x\sqrt{5}+x\sqrt{2}=0$$

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

$$2x-2\sqrt{5}+3-x\sqrt{5}+x\sqrt{2}=-2\sqrt{2}$$

Add 2\sqrt{5} to both sides.

$$2x+3-x\sqrt{5}+x\sqrt{2}=-2\sqrt{2}+2\sqrt{5}$$

Subtract 3 from both sides.

$$2x-x\sqrt{5}+x\sqrt{2}=-2\sqrt{2}+2\sqrt{5}-3$$

Combine all terms containing x.

$$\left(2-\sqrt{5}+\sqrt{2}\right)x=-2\sqrt{2}+2\sqrt{5}-3$$

The equation is in standard form.

$$\left(\sqrt{2}+2-\sqrt{5}\right)x=2\sqrt{5}-2\sqrt{2}-3$$

Divide both sides by 2-\sqrt{5}+\sqrt{2}.

$$\frac{\left(\sqrt{2}+2-\sqrt{5}\right)x}{\sqrt{2}+2-\sqrt{5}}=\frac{2\sqrt{5}-2\sqrt{2}-3}{\sqrt{2}+2-\sqrt{5}}$$

Dividing by 2-\sqrt{5}+\sqrt{2} undoes the multiplication by 2-\sqrt{5}+\sqrt{2}.

$$x=\frac{2\sqrt{5}-2\sqrt{2}-3}{\sqrt{2}+2-\sqrt{5}}$$

Divide -2\sqrt{2}+2\sqrt{5}-3 by 2-\sqrt{5}+\sqrt{2}.

$$x=\frac{4\sqrt{10}+7\sqrt{2}-\sqrt{5}-56}{31}$$