Solve sqrt{135}-xsqrt{3}=-2sqrt{15}

$$\sqrt { 135 } - x \sqrt { 3 } = - 2 \sqrt { 15 }$$

Solve for x

$$x=5\sqrt{5}\approx 11.180339887$$

Steps for Solving Linear Equation

Factor 135=3^{2}\times 15. Rewrite the square root of the product \sqrt{3^{2}\times 15} as the product of square roots \sqrt{3^{2}}\sqrt{15}. Take the square root of 3^{2}.

$$3\sqrt{15}-x\sqrt{3}=-2\sqrt{15}$$

Subtract 3\sqrt{15} from both sides.

$$-x\sqrt{3}=-2\sqrt{15}-3\sqrt{15}$$

Combine -2\sqrt{15} and -3\sqrt{15} to get -5\sqrt{15}.

$$-x\sqrt{3}=-5\sqrt{15}$$

The equation is in standard form.

$$\left(-\sqrt{3}\right)x=-5\sqrt{15}$$

Divide both sides by -\sqrt{3}.

$$\frac{\left(-\sqrt{3}\right)x}{-\sqrt{3}}=-\frac{5\sqrt{15}}{-\sqrt{3}}$$

Dividing by -\sqrt{3} undoes the multiplication by -\sqrt{3}.

$$x=-\frac{5\sqrt{15}}{-\sqrt{3}}$$

Divide -5\sqrt{15} by -\sqrt{3}.

$$x=5\sqrt{5}$$