Solve 80+40sqrt{2}=(5+5+5sqrt{2})x

$$80+40 \sqrt{ 2 } = (5+5+5 \sqrt{ 2 } )x$$

Solve for x

$$x=8$$

Steps for Solving Linear Equation

Add 5 and 5 to get 10.

$$80+40\sqrt{2}=\left(10+5\sqrt{2}\right)x$$

Use the distributive property to multiply 10+5\sqrt{2} by x.

$$80+40\sqrt{2}=10x+5\sqrt{2}x$$

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

$$10x+5\sqrt{2}x=80+40\sqrt{2}$$

Combine all terms containing x.

$$\left(10+5\sqrt{2}\right)x=80+40\sqrt{2}$$

The equation is in standard form.

$$\left(5\sqrt{2}+10\right)x=40\sqrt{2}+80$$

Divide both sides by 10+5\sqrt{2}.

$$\frac{\left(5\sqrt{2}+10\right)x}{5\sqrt{2}+10}=\frac{40\sqrt{2}+80}{5\sqrt{2}+10}$$

Dividing by 10+5\sqrt{2} undoes the multiplication by 10+5\sqrt{2}.

$$x=\frac{40\sqrt{2}+80}{5\sqrt{2}+10}$$

Divide 80+40\sqrt{2} by 10+5\sqrt{2}.

$$x=8$$