Solve x^2-192=0

$$x ^ { 2 } - 192 = 0$$

Solve for x

$$x=8\sqrt{3}\approx 13.856406461$$

$$x=-8\sqrt{3}\approx -13.856406461$$

Steps by Finding Square Root

Add 192 to both sides. Anything plus zero gives itself.

$$x^{2}=192$$

Take the square root of both sides of the equation.

$$x=8\sqrt{3} x=-8\sqrt{3}$$

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.

$$x^{2}-192=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -192 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-192\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-192\right)}}{2}$$

Multiply -4 times -192.

$$x=\frac{0±\sqrt{768}}{2}$$

Take the square root of 768.

$$x=\frac{0±16\sqrt{3}}{2}$$

Now solve the equation x=\frac{0±16\sqrt{3}}{2} when ± is plus.

$$x=8\sqrt{3}$$

Now solve the equation x=\frac{0±16\sqrt{3}}{2} when ± is minus.

$$x=-8\sqrt{3}$$

The equation is now solved.

$$x=8\sqrt{3} x=-8\sqrt{3}$$