Solve 2(x-sqrt{32})=98-x

$$2 ( x - \sqrt { 32 } ) = 98 - x$$

Solve for x

$$x = \frac{8 \sqrt{2} + 98}{3} \approx 36.437902833$$

Steps for Solving Linear Equation

Factor 32=4^{2}\times 2. Rewrite the square root of the product \sqrt{4^{2}\times 2} as the product of square roots \sqrt{4^{2}}\sqrt{2}. Take the square root of 4^{2}.

$$2\left(x-4\sqrt{2}\right)=98-x$$

Use the distributive property to multiply 2 by x-4\sqrt{2}.

$$2x-8\sqrt{2}=98-x$$

Add x to both sides.

$$2x-8\sqrt{2}+x=98$$

Combine 2x and x to get 3x.

$$3x-8\sqrt{2}=98$$

Add 8\sqrt{2} to both sides.

$$3x=98+8\sqrt{2}$$

The equation is in standard form.

$$3x=8\sqrt{2}+98$$

Divide both sides by 3.

$$\frac{3x}{3}=\frac{8\sqrt{2}+98}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$x=\frac{8\sqrt{2}+98}{3}$$