Solve sqrt{40}=-xsqrt{10}dx=

$$\sqrt { 40 } = - x \sqrt { 10 } d x =$$

Solve for d

$$d=-\frac{2}{x^{2}}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Factor 40=2^{2}\times 10. Rewrite the square root of the product \sqrt{2^{2}\times 10} as the product of square roots \sqrt{2^{2}}\sqrt{10}. Take the square root of 2^{2}.

$$2\sqrt{10}=\left(-x\right)\sqrt{10}dx$$

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

$$\left(-x\right)\sqrt{10}dx=2\sqrt{10}$$

Multiply x and x to get x^{2}.

$$-x^{2}\sqrt{10}d=2\sqrt{10}$$

The equation is in standard form.

$$\left(-\sqrt{10}x^{2}\right)d=2\sqrt{10}$$

Divide both sides by -x^{2}\sqrt{10}.

$$\frac{\left(-\sqrt{10}x^{2}\right)d}{-\sqrt{10}x^{2}}=\frac{2\sqrt{10}}{-\sqrt{10}x^{2}}$$

Dividing by -x^{2}\sqrt{10} undoes the multiplication by -x^{2}\sqrt{10}.

$$d=\frac{2\sqrt{10}}{-\sqrt{10}x^{2}}$$

Divide 2\sqrt{10} by -x^{2}\sqrt{10}.

$$d=-\frac{2}{x^{2}}$$

Solve for x (complex solution)

$$x=-\sqrt{2}id^{-\frac{1}{2}}$$

$$x=\sqrt{2}id^{-\frac{1}{2}}\text{, }d\neq 0$$

Solve for x

$$x=\sqrt{-\frac{2}{d}}$$

$$x=-\sqrt{-\frac{2}{d}}\text{, }d<0$$