Solve x^2=14400

$${ x }^{ 2 } =14400$$

Solve for x

$$x=120$$

$$x=-120$$

Steps Using Difference of Squares

Subtract 14400 from both sides.

$$x^{2}-14400=0$$

Consider x^{2}-14400. Rewrite x^{2}-14400 as x^{2}-120^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-120\right)\left(x+120\right)=0$$

To find equation solutions, solve x-120=0 and x+120=0.

$$x=120 x=-120$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$x=120 x=-120$$

Steps Using the Quadratic Formula

Subtract 14400 from both sides.

$$x^{2}-14400=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -14400 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-14400\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-14400\right)}}{2}$$

Multiply -4 times -14400.

$$x=\frac{0±\sqrt{57600}}{2}$$

Take the square root of 57600.

$$x=\frac{0±240}{2}$$

Now solve the equation x=\frac{0±240}{2} when ± is plus. Divide 240 by 2.

$$x=120$$

Now solve the equation x=\frac{0±240}{2} when ± is minus. Divide -240 by 2.

$$x=-120$$

The equation is now solved.

$$x=120 x=-120$$