Solve 200=x^20.5

$$200= { x }^{ 2 } 0.5$$

Solve for x

$$x=20$$

$$x=-20$$

Steps Using Difference of Squares

Divide both sides by 0.5.

$$\frac{200}{0.5}=x^{2}$$

Expand \frac{200}{0.5} by multiplying both numerator and the denominator by 10.

$$\frac{2000}{5}=x^{2}$$

Divide 2000 by 5 to get 400.

$$400=x^{2}$$

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

$$x^{2}=400$$

Subtract 400 from both sides.

$$x^{2}-400=0$$

Consider x^{2}-400. Rewrite x^{2}-400 as x^{2}-20^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-20\right)\left(x+20\right)=0$$

To find equation solutions, solve x-20=0 and x+20=0.

$$x=20 x=-20$$

Steps by Finding Square Root

Divide both sides by 0.5.

$$\frac{200}{0.5}=x^{2}$$

Expand \frac{200}{0.5} by multiplying both numerator and the denominator by 10.

$$\frac{2000}{5}=x^{2}$$

Divide 2000 by 5 to get 400.

$$400=x^{2}$$

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

$$x^{2}=400$$

Take the square root of both sides of the equation.

$$x=20 x=-20$$

Steps Using the Quadratic Formula

Divide both sides by 0.5.

$$\frac{200}{0.5}=x^{2}$$

Expand \frac{200}{0.5} by multiplying both numerator and the denominator by 10.

$$\frac{2000}{5}=x^{2}$$

Divide 2000 by 5 to get 400.

$$400=x^{2}$$

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

$$x^{2}=400$$

Subtract 400 from both sides.

$$x^{2}-400=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -400 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-400\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-400\right)}}{2}$$

Multiply -4 times -400.

$$x=\frac{0±\sqrt{1600}}{2}$$

Take the square root of 1600.

$$x=\frac{0±40}{2}$$

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

$$x=20$$

Now solve the equation x=\frac{0±40}{2} when ± is minus. Divide -40 by 2.

$$x=-20$$

The equation is now solved.

$$x=20 x=-20$$