Solve y=sqrt{98}-sqrt{32}-sqrt{8}er

$$y = \sqrt { 98 } - \sqrt { 32 } - \sqrt { 8 } er$$

Solve for r

$$r=\frac{-\sqrt{2}y+6}{4e}$$

Steps for Solving Linear Equation

Factor 98=7^{2}\times 2. Rewrite the square root of the product \sqrt{7^{2}\times 2} as the product of square roots \sqrt{7^{2}}\sqrt{2}. Take the square root of 7^{2}.

$$y=7\sqrt{2}-\sqrt{32}-\sqrt{8}er$$

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}.

$$y=7\sqrt{2}-4\sqrt{2}-\sqrt{8}er$$

Combine 7\sqrt{2} and -4\sqrt{2} to get 3\sqrt{2}.

$$y=3\sqrt{2}-\sqrt{8}er$$

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}.

$$y=3\sqrt{2}-2\sqrt{2}er$$

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

$$3\sqrt{2}-2\sqrt{2}er=y$$

Subtract 3\sqrt{2} from both sides.

$$-2\sqrt{2}er=y-3\sqrt{2}$$

The equation is in standard form.

$$\left(-2e\sqrt{2}\right)r=y-3\sqrt{2}$$

Divide both sides by -2\sqrt{2}e.

$$\frac{\left(-2e\sqrt{2}\right)r}{-2e\sqrt{2}}=\frac{y-3\sqrt{2}}{-2e\sqrt{2}}$$

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

$$r=\frac{y-3\sqrt{2}}{-2e\sqrt{2}}$$

Divide y-3\sqrt{2} by -2\sqrt{2}e.

$$r=\frac{-\frac{\sqrt{2}y}{4}+\frac{3}{2}}{e}$$

Solve for y

$$y=-\sqrt{2}\left(2er-3\right)$$

Solution Steps

Factor 98=7^{2}\times 2. Rewrite the square root of the product \sqrt{7^{2}\times 2} as the product of square roots \sqrt{7^{2}}\sqrt{2}. Take the square root of 7^{2}.

$$y=7\sqrt{2}-\sqrt{32}-\sqrt{8}er$$

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}.

$$y=7\sqrt{2}-4\sqrt{2}-\sqrt{8}er$$

Combine 7\sqrt{2} and -4\sqrt{2} to get 3\sqrt{2}.

$$y=3\sqrt{2}-\sqrt{8}er$$

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}.

$$y=3\sqrt{2}-2\sqrt{2}er$$