Solve 100/2=x^2/10^2

$$\frac { 100 } { 2 } = \frac { x ^ { 2 } } { 10 ^ { 2 } }$$

Solve for x

$$x=50\sqrt{2}\approx 70.710678119$$

$$x=-50\sqrt{2}\approx -70.710678119$$

Steps by Finding Square Root

Divide 100 by 2 to get 50.

$$50=\frac{x^{2}}{10^{2}}$$

Calculate 10 to the power of 2 and get 100.

$$50=\frac{x^{2}}{100}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{x^{2}}{100}=50$$

Multiply both sides by 100.

$$x^{2}=50\times 100$$

Multiply 50 and 100 to get 5000.

$$x^{2}=5000$$

Take the square root of both sides of the equation.

$$x=50\sqrt{2} x=-50\sqrt{2}$$

Steps Using the Quadratic Formula

Divide 100 by 2 to get 50.

$$50=\frac{x^{2}}{10^{2}}$$

Calculate 10 to the power of 2 and get 100.

$$50=\frac{x^{2}}{100}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{x^{2}}{100}=50$$

Subtract 50 from both sides.

$$\frac{x^{2}}{100}-50=0$$

Multiply both sides of the equation by 100.

$$x^{2}-5000=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -5000 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-5000\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-5000\right)}}{2}$$

Multiply -4 times -5000.

$$x=\frac{0±\sqrt{20000}}{2}$$

Take the square root of 20000.

$$x=\frac{0±100\sqrt{2}}{2}$$

Now solve the equation x=\frac{0±100\sqrt{2}}{2} when ± is plus.

$$x=50\sqrt{2}$$

Now solve the equation x=\frac{0±100\sqrt{2}}{2} when ± is minus.

$$x=-50\sqrt{2}$$

The equation is now solved.

$$x=50\sqrt{2} x=-50\sqrt{2}$$