Solve u^2-2=0

$$u ^ { 2 } - 2 = 0$$

Solve for u

$$u=\sqrt{2}\approx 1.414213562$$

$$u=-\sqrt{2}\approx -1.414213562$$

Steps by Finding Square Root

Add 2 to both sides. Anything plus zero gives itself.

$$u^{2}=2$$

Take the square root of both sides of the equation.

$$u=\sqrt{2} u=-\sqrt{2}$$

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.

$$u^{2}-2=0$$

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

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

Square 0.

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

Multiply -4 times -2.

$$u=\frac{0±\sqrt{8}}{2}$$

Take the square root of 8.

$$u=\frac{0±2\sqrt{2}}{2}$$

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

$$u=\sqrt{2}$$

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

$$u=-\sqrt{2}$$

The equation is now solved.

$$u=\sqrt{2} u=-\sqrt{2}$$