Solve x^2=10^2*20^2

$${ x }^{ 2 } = { 10 }^{ 2 } \times { 20 }^{ 2 }$$

Solve for x

$$x=200$$

$$x=-200$$

Steps Using Difference of Squares

Calculate 10 to the power of 2 and get 100.

$$x^{2}=100\times 20^{2}$$

Calculate 20 to the power of 2 and get 400.

$$x^{2}=100\times 400$$

Multiply 100 and 400 to get 40000.

$$x^{2}=40000$$

Subtract 40000 from both sides.

$$x^{2}-40000=0$$

Consider x^{2}-40000. Rewrite x^{2}-40000 as x^{2}-200^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-200\right)\left(x+200\right)=0$$

To find equation solutions, solve x-200=0 and x+200=0.

$$x=200 x=-200$$

Steps by Finding Square Root

Calculate 10 to the power of 2 and get 100.

$$x^{2}=100\times 20^{2}$$

Calculate 20 to the power of 2 and get 400.

$$x^{2}=100\times 400$$

Multiply 100 and 400 to get 40000.

$$x^{2}=40000$$

Take the square root of both sides of the equation.

$$x=200 x=-200$$

Steps Using the Quadratic Formula

Calculate 10 to the power of 2 and get 100.

$$x^{2}=100\times 20^{2}$$

Calculate 20 to the power of 2 and get 400.

$$x^{2}=100\times 400$$

Multiply 100 and 400 to get 40000.

$$x^{2}=40000$$

Subtract 40000 from both sides.

$$x^{2}-40000=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -40000 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-40000\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-40000\right)}}{2}$$

Multiply -4 times -40000.

$$x=\frac{0±\sqrt{160000}}{2}$$

Take the square root of 160000.

$$x=\frac{0±400}{2}$$

Now solve the equation x=\frac{0±400}{2} when ± is plus. Divide 400 by 2.

$$x=200$$

Now solve the equation x=\frac{0±400}{2} when ± is minus. Divide -400 by 2.

$$x=-200$$

The equation is now solved.

$$x=200 x=-200$$