Solve x^2=16400

$${ x }^{ 2 } =16400$$

Solve for x

$$x=20\sqrt{41}\approx 128.062484749$$

$$x=-20\sqrt{41}\approx -128.062484749$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$x=20\sqrt{41} x=-20\sqrt{41}$$

Steps Using the Quadratic Formula

Subtract 16400 from both sides.

$$x^{2}-16400=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -16400 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-16400\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-16400\right)}}{2}$$

Multiply -4 times -16400.

$$x=\frac{0±\sqrt{65600}}{2}$$

Take the square root of 65600.

$$x=\frac{0±40\sqrt{41}}{2}$$

Now solve the equation x=\frac{0±40\sqrt{41}}{2} when ± is plus.

$$x=20\sqrt{41}$$

Now solve the equation x=\frac{0±40\sqrt{41}}{2} when ± is minus.

$$x=-20\sqrt{41}$$

The equation is now solved.

$$x=20\sqrt{41} x=-20\sqrt{41}$$