Solve x^2=200(62*62-38*38)^2/100*100*100*100=

$$x ^ { 2 } = \frac { 200 ( 62 \times 62 - 38 \times 38 ) ^ { 2 } } { 100 \times 100 \times 100 \times 100 } =$$

Solve for x

$$x = \frac{12 \sqrt{2}}{5} \approx 3.39411255$$

$$x = -\frac{12 \sqrt{2}}{5} \approx -3.39411255$$

Steps by Finding Square Root

Cancel out 2\times 100 in both numerator and denominator.

$$x^{2}=\frac{\left(62\times 62-38\times 38\right)^{2}}{50\times 100\times 100}$$

Multiply 62 and 62 to get 3844.

$$x^{2}=\frac{\left(3844-38\times 38\right)^{2}}{50\times 100\times 100}$$

Multiply 38 and 38 to get 1444.

$$x^{2}=\frac{\left(3844-1444\right)^{2}}{50\times 100\times 100}$$

Subtract 1444 from 3844 to get 2400.

$$x^{2}=\frac{2400^{2}}{50\times 100\times 100}$$

Calculate 2400 to the power of 2 and get 5760000.

$$x^{2}=\frac{5760000}{50\times 100\times 100}$$

Multiply 50 and 100 to get 5000.

$$x^{2}=\frac{5760000}{5000\times 100}$$

Multiply 5000 and 100 to get 500000.

$$x^{2}=\frac{5760000}{500000}$$

Reduce the fraction \frac{5760000}{500000} to lowest terms by extracting and canceling out 20000.

$$x^{2}=\frac{288}{25}$$

Take the square root of both sides of the equation.

$$x=\frac{12\sqrt{2}}{5} x=-\frac{12\sqrt{2}}{5}$$

Steps Using the Quadratic Formula

Cancel out 2\times 100 in both numerator and denominator.

$$x^{2}=\frac{\left(62\times 62-38\times 38\right)^{2}}{50\times 100\times 100}$$

Multiply 62 and 62 to get 3844.

$$x^{2}=\frac{\left(3844-38\times 38\right)^{2}}{50\times 100\times 100}$$

Multiply 38 and 38 to get 1444.

$$x^{2}=\frac{\left(3844-1444\right)^{2}}{50\times 100\times 100}$$

Subtract 1444 from 3844 to get 2400.

$$x^{2}=\frac{2400^{2}}{50\times 100\times 100}$$

Calculate 2400 to the power of 2 and get 5760000.

$$x^{2}=\frac{5760000}{50\times 100\times 100}$$

Multiply 50 and 100 to get 5000.

$$x^{2}=\frac{5760000}{5000\times 100}$$

Multiply 5000 and 100 to get 500000.

$$x^{2}=\frac{5760000}{500000}$$

Reduce the fraction \frac{5760000}{500000} to lowest terms by extracting and canceling out 20000.

$$x^{2}=\frac{288}{25}$$

Subtract \frac{288}{25} from both sides.

$$x^{2}-\frac{288}{25}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{288}{25} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{288}{25}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{288}{25}\right)}}{2}$$

Multiply -4 times -\frac{288}{25}.

$$x=\frac{0±\sqrt{\frac{1152}{25}}}{2}$$

Take the square root of \frac{1152}{25}.

$$x=\frac{0±\frac{24\sqrt{2}}{5}}{2}$$

Now solve the equation x=\frac{0±\frac{24\sqrt{2}}{5}}{2} when ± is plus.

$$x=\frac{12\sqrt{2}}{5}$$

Now solve the equation x=\frac{0±\frac{24\sqrt{2}}{5}}{2} when ± is minus.

$$x=-\frac{12\sqrt{2}}{5}$$

The equation is now solved.

$$x=\frac{12\sqrt{2}}{5} x=-\frac{12\sqrt{2}}{5}$$