Solve x^2+left(800-x^2/2500right)left(800-x^2/2500right)

$${ x }^{ 2 } + \left( 800- \frac{ { x }^{ 2 } }{ 2500 } \right) \left( 800- \frac{ { x }^{ 2 } }{ 2500 } \right)$$

Evaluate

$$\frac{x^{4}}{6250000}+\frac{9x^{2}}{25}+640000$$

Short Solution Steps

Multiply 800-\frac{x^{2}}{2500} and 800-\frac{x^{2}}{2500} to get \left(800-\frac{x^{2}}{2500}\right)^{2}.

$$x^{2}+\left(800-\frac{x^{2}}{2500}\right)^{2}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 800 times \frac{2500}{2500}.

$$x^{2}+\left(\frac{800\times 2500}{2500}-\frac{x^{2}}{2500}\right)^{2}$$

Since \frac{800\times 2500}{2500} and \frac{x^{2}}{2500} have the same denominator, subtract them by subtracting their numerators.

$$x^{2}+\left(\frac{800\times 2500-x^{2}}{2500}\right)^{2}$$

Do the multiplications in 800\times 2500-x^{2}.

$$x^{2}+\left(\frac{2000000-x^{2}}{2500}\right)^{2}$$

To raise \frac{2000000-x^{2}}{2500} to a power, raise both numerator and denominator to the power and then divide.

$$x^{2}+\frac{\left(2000000-x^{2}\right)^{2}}{2500^{2}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x^{2} times \frac{2500^{2}}{2500^{2}}.

$$\frac{x^{2}\times 2500^{2}}{2500^{2}}+\frac{\left(2000000-x^{2}\right)^{2}}{2500^{2}}$$

Since \frac{x^{2}\times 2500^{2}}{2500^{2}} and \frac{\left(2000000-x^{2}\right)^{2}}{2500^{2}} have the same denominator, add them by adding their numerators.

$$\frac{x^{2}\times 2500^{2}+\left(2000000-x^{2}\right)^{2}}{2500^{2}}$$

Do the multiplications in x^{2}\times 2500^{2}+\left(2000000-x^{2}\right)^{2}.

$$\frac{6250000x^{2}[phone]-4000000x^{2}+x^{4}}{2500^{2}}$$

Combine like terms in 6250000x^{2}[phone]-4000000x^{2}+x^{4}.

$$\frac{2250000x^{2}[phone]+x^{4}}{2500^{2}}$$

Expand 2500^{2}.

$$\frac{2250000x^{2}[phone]+x^{4}}{6250000}$$

Expand

$$\frac{x^{4}}{6250000}+\frac{9x^{2}}{25}+640000$$

Short Solution Steps

Multiply 800-\frac{x^{2}}{2500} and 800-\frac{x^{2}}{2500} to get \left(800-\frac{x^{2}}{2500}\right)^{2}.

$$x^{2}+\left(800-\frac{x^{2}}{2500}\right)^{2}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 800 times \frac{2500}{2500}.

$$x^{2}+\left(\frac{800\times 2500}{2500}-\frac{x^{2}}{2500}\right)^{2}$$

Since \frac{800\times 2500}{2500} and \frac{x^{2}}{2500} have the same denominator, subtract them by subtracting their numerators.

$$x^{2}+\left(\frac{800\times 2500-x^{2}}{2500}\right)^{2}$$

Do the multiplications in 800\times 2500-x^{2}.

$$x^{2}+\left(\frac{2000000-x^{2}}{2500}\right)^{2}$$

To raise \frac{2000000-x^{2}}{2500} to a power, raise both numerator and denominator to the power and then divide.

$$x^{2}+\frac{\left(2000000-x^{2}\right)^{2}}{2500^{2}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x^{2} times \frac{2500^{2}}{2500^{2}}.

$$\frac{x^{2}\times 2500^{2}}{2500^{2}}+\frac{\left(2000000-x^{2}\right)^{2}}{2500^{2}}$$

Since \frac{x^{2}\times 2500^{2}}{2500^{2}} and \frac{\left(2000000-x^{2}\right)^{2}}{2500^{2}} have the same denominator, add them by adding their numerators.

$$\frac{x^{2}\times 2500^{2}+\left(2000000-x^{2}\right)^{2}}{2500^{2}}$$

Do the multiplications in x^{2}\times 2500^{2}+\left(2000000-x^{2}\right)^{2}.

$$\frac{6250000x^{2}[phone]-4000000x^{2}+x^{4}}{2500^{2}}$$

Combine like terms in 6250000x^{2}[phone]-4000000x^{2}+x^{4}.

$$\frac{2250000x^{2}[phone]+x^{4}}{2500^{2}}$$

Expand 2500^{2}.

$$\frac{2250000x^{2}[phone]+x^{4}}{6250000}$$