Solve x^2=e

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

Solve for x

$$x=\sqrt{e}\approx 1.648721271$$

$$x=-\sqrt{e}\approx -1.648721271$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

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.

$$x^{2}=e$$

Subtract e from both sides of the equation.

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

Subtracting e from itself leaves 0.

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

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

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

Square 0.

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

Multiply -4 times -e.

$$x=\frac{0±\sqrt{4e}}{2}$$

Take the square root of 4e.

$$x=\frac{0±2\sqrt{e}}{2}$$

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

$$x=\sqrt{e}$$

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

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

The equation is now solved.

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