Solve xex-1=0

$$xex-1=0$$

Solve for x

$$x=\frac{1}{\sqrt{e}}\approx 0.60653066$$

$$x=-\frac{1}{\sqrt{e}}\approx -0.60653066$$

Steps by Finding Square Root

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

$$x^{2}e-1=0$$

Add 1 to both sides. Anything plus zero gives itself.

$$x^{2}e=1$$

Divide both sides by e.

$$\frac{ex^{2}}{e}=\frac{1}{e}$$

Dividing by e undoes the multiplication by e.

$$x^{2}=\frac{1}{e}$$

Take the square root of both sides of the equation.

$$x=\frac{1}{\sqrt{e}} x=-\frac{1}{\sqrt{e}}$$

Steps Using the Quadratic Formula

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

$$x^{2}e-1=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$ex^{2}-1=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute e for a, 0 for b, and -1 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4e\left(-1\right)}}{2e}$$

Square 0.

$$x=\frac{0±\sqrt{-4e\left(-1\right)}}{2e}$$

Multiply -4 times e.

$$x=\frac{0±\sqrt{\left(-4e\right)\left(-1\right)}}{2e}$$

Multiply -4e times -1.

$$x=\frac{0±\sqrt{4e}}{2e}$$

Take the square root of 4e.

$$x=\frac{0±2\sqrt{e}}{2e}$$

Now solve the equation x=\frac{0±2\sqrt{e}}{2e} when ± is plus.

$$x=\frac{1}{\sqrt{e}}$$

Now solve the equation x=\frac{0±2\sqrt{e}}{2e} when ± is minus.

$$x=-\frac{1}{\sqrt{e}}$$

The equation is now solved.

$$x=\frac{1}{\sqrt{e}} x=-\frac{1}{\sqrt{e}}$$